Decomposable functors and the exponential principle, II (2009)
Cameron, Peter, Krattenthaler, Christian, Müller, Thomas W.
We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach...
Some determinants of path generating functions (2009)
Krattenthaler, Christian, Cigler, Johann
We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By...
Summation formulas for GJMS-operators and Q-curvatures on the Moebius sphere (2009)
Juhl, Andreas, Krattenthaler, Christian
For the Moebius sphere $\S^{q,p}$, we confirm the recursive formulas for GJMS-operators and $Q$-curvatures formulated by the first author in "On conformally covariant powers of the Laplacian"...
Stanley decompositions and Hilbert depth in the Koszul complex (2009)
Bruns, Winfried, Krattenthaler, Christian, Uliczka, Jan
Stanley decompositions of multigraded modules $M$ over polynomials rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition,...
On the integrality of the Taylor coefficients of mirror maps (2009)
Krattenthaler, Christian, Rivoal, Tanguy
We show that the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$ are integers, where ${\bf F}(z)$ and ${\bf G}(z)+\log(z) {\bf F}(z)$ are specific solutions of certain...
On the integrality of the Taylor coefficients of mirror maps, II (2009)
Krattenthaler, Christian, Rivoal, Tanguy
We continue our study begun in ``On the integrality of the Taylor coefficients of mirror maps'' (arXiv:0907.2577) of the fine integrality properties of the Taylor coefficients of the series ${\bf...
D\'emonstration de l'Observation 2 d'Almkvist et Zudilin (2009)
Krattenthaler, Christian, Rivoal, Tanguy
We prove Obnservation 2 in arXiv:math/0402386 by Gert Almkvist and Wadim Zudilin.
The poset of bipartitions (2009)
Hetyei, Gábor, Krattenthaler, Christian
Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We...
Euler characteristic of the truncated order complex of generalized noncrossing partitions (2009)
Armstrong, Drew, Krattenthaler, Christian
The purpose of this note is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In...
On the non-quadraticity of values of the q-exponential function and related q-series (2008)
Krattenthaler, Christian, Rochev, Igor, Vaananen, Keijo, Zudilin, Wadim
We investigate arithmetic properties of values of the entire function $$ F(z)=F_q(z;\lambda)=\sum_{n=0}^\infty\frac{z^n}{\prod_{j=1}^n(q^j-\lambda)}, \qquad |q|>1, \quad \lambda\notin q^{\mathbb...
Ciucu, Mihai, Krattenthaler, Christian
We prove that a Schur function of rectangular shape $(M^n)$ whose variables are specialized to $x_1,x_1^{-1},...,x_n,x_n^{-1}$ factorizes into a product of two odd orthogonal characters of...
On a linear form for Catalan's constant (2008)
Krattenthaler, Christian, Rivoal, Tanguy
It is shown how Andrews' multidimensional extension of Watson's transformation between a very-well-poised $_8\phi_7$-series and a balanced $_4\phi_3$-series can be used to give a straightforward...
On the integrality of Taylor coefficients of mirror maps in several variables (2008)
Krattenthaler, Christian, Rivoal, Tanguy
With $\bz=(z_1,z_2,...,z_d)$, we show that the Taylor coefficients of the multi-variable series $q(\bz)=z_i\exp(G(\bz)/F(\bz))$ are integers, where $F(\bz)$ and $G(\bz)+\log(z_i) F(\bz)$,...
George E. Andrews, Christian Krattenthaler, Luigi Orsina, Paolo Papi
Abstract. We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1, C). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas...
Algebraic combinatorics in Vienna (2008)
The Vienna, Christian Krattenthaler, Markus Fulmek
Prohaska. The investigations mainly concentrated on the combinatorics of tableaux and nonintersecting lattice paths and can be roughly divided into four topics: (I) Counting nonintersecting lattice...
The flagged Cauchy determinant (2008)
Abstract. We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard...
Parity patterns associated with lifts of Hecke groups (2008)
Krattenthaler, Christian, Müller, Thomas W.
Let $q$ be an odd prime, $m$ a positive integer, and let $\Ga_m(q)$ be the group generated by two elements $x$ and $y$ subject to the relations $x^{2m}=y^{qm}=1$ and $x^2=y^q$; that is, $\Ga_m(q)$ is...
The Hilbert Series of Pfaffian Rings (2008)
Sudhir R. Ghorpade, Christian Krattenthaler
We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An appendix outlining some...
Regular sequences of symmetric polynomials (2008)
Conca, Aldo, Krattenthaler, Christian, Watanabe, Junzo
Denote by p_k the k-th power sum symmetric polynomial n variables. The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power...
Algebraic combinatorics in Vienna (2007)
The Vienna, Christian Krattenthaler, Markus Fulmek
Prohaska. The investigations mainly concentrated on the combinatorics of tableaux and nonintersecting lattice paths and can be roughly divided into four topics: (I) Counting nonintersecting lattice...
Symmetry Classes Mihai, Mihai Ciucu, Christian Krattenthaler
. We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation,...
Rectangular Scott-type Permanents (2007)
Guo-niu Han, Christian Krattenthaler
. --- Let x 1 ; x 2 ; : : : ; xn be the zeroes of a polynomial P (x) of degree n and y 1 ; y 2 ; : : : ; ym be the zeroes of another polynomial Q(y) of degree m. Our object of study is the permanent...
Sudhir R. Ghorpade, Christian Krattenthaler
Dedicated to Professor Shreeram Abhyankar on his seventieth birthday Abstract. We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaan ring, and a...
y Institut fur Mathematik der Universitat Wien, (2007)
Gert Almkvist, Christian Krattenthaler, Joakim Petersson
Abstract. We show how to nd series expansions for of the form
Enumeration of ad-nilpotent b-ideals for simple Lie algebras, in preparation (2007)
Christian Krattenthaler, Luigi Orsina, Paolo Papi
Dedicated to the memory of Rodica Simion Abstract. We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having xed class of...
PLANE PARTITIONS II: 5 1 (2007)
Mihai Ciucu, Christian Krattenthaler
Abstract. We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant...
Enumeration of lozenge tilings of hexagons with cut off corners, in preparation. (p (2007)
Mihai Ciucu, Christian Krattenthaler
Abstract. Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating...
George E. Andrews, Christian Krattenthaler, Luigi Orsina, Paolo Papi
Abstract. We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1; C). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas...
Gert Almkvist Christian, Christian Krattenthaler, Joakim Petersson
We show how to nd series expansions for of the form , where S(n) is some polynomial in n (depending on m; p; a). We prove that there exist such expansions for m = 8k, p = 4k, a = ( 4) , for any k,...
ad-NILPOTENT b-IDEALS IN sl(n) HAVING A FIXED CLASS OF (2007)
Nilpotence Combinatorics And, George E. Andrews, Christian Krattenthaler, Luigi Orsina, Paolo Papi
We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1; C ). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the...
Determinants of (generalised) Catalan numbers (2007)
We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindstr\"om-Gessel-Viennot theorem on...
On the integrality of the Taylor coefficients of mirror maps (2007)
Krattenthaler, Christian, Rivoal, Tanguy
We show that the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$ are integers, where ${\bf F}(z)$ and ${\bf G}(z)+\log(z) {\bf F}(z)$ are specific solutions of certain...
Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions (2007)
Krattenthaler, Christian, Müller, Thomas
Given a finite irreducible Coxeter group $W$, a positive integer $d$, and types $T_1,T_2,...,T_d$ (in the sense of the classification of finite Coxeter groups), we compute the number of...
Recent progress in the study of representations of integers as sums of squares (2007)
Chan, Heng Huat, Krattenthaler, Christian
In this article, we collect the recent results concerning the representations of integers as sums of an even number of squares that are inspired by conjectures of Kac and Wakimoto. We start with a...
On the number of fully packed loop configurations with a fixed associated matching (2007)
Caselli, Fabrizio, Krattenthaler, Christian, Lass, Bodo, Nadeau, Philippe
We show that the number of fully packed loop configurations corresponding to a matching with $m$ nested arches is polynomial in $m$ if $m$ is large enough, thus essentially proving two conjectures by...
An Entry of Ramanujan on Hypergeometric Series in his Notebooks (2006)
Rao, K. Srinivasa, Berghe, G. Vanden, Krattenthaler, Christian
Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for $_3F_2(a,a,x;1+a,1+a+N;1)$, where $N$ is a non-negative...
Non-commutative Hopf algebra of formal diffeomorphisms (2006)
Brouder, Christian, Frabetti, Alessandra, Krattenthaler, Christian
The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the...
How can we escape Thomae's relations? (2006)
KRATTENTHALER, Christian, RIVOAL, Tanguy
In 1879, Thomae discussed the relations between two generic hypergeometric $_3F_2$-series with argument 1. It is well-known since then that, in combination with the trivial ones which come from...
The $M$-triangle of generalised non-crossing partitions for the types $E_7$ and $E_8$ (2006)
The $M$-triangle of a ranked locally finite poset $P$ is the generating function $\sum_{u,w\in P} ^{}\mu(u,w) x^{\rk u}y^{\rk w}$, where $\mu(.,.)$ is the M\"obius function of $P$. We compute the...
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes (2005)
We put recent results by Chen, Deng, Du, Stanley and Yan on crossings and nestings of matchings and set partitions in the larger context of the enumeration of fillings of Ferrers shape on which one...
The $F$-triangle of the generalised cluster complex (2005)
The $F$-triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the $F$-triangle explicitly for all irreducible finite root systems. Furthermore, we use...
2-adic valuations of certain ratios of products of factorials and applications (2005)
Friedland, Shmuel, Krattenthaler, Christian
We prove the conjecture of Falikman--Friedland--Loewy on the parity of the degrees of projective varieties of $n\times n$ complex symmetric matrices of rank at most $k$. We also characterize the...
Watermelon configurations with wall interaction: exact and asymptotic results (2005)
We perform an exact and asymptotic analysis of the model of $n$ vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we...
Advanced Determinant Calculus: A Complement (2005)
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my...
On the number of fully packed loop configurations with a fixed associated matching (2005)
Caselli, Fabrizio, Krattenthaler, Christian, Lass, Bodo, Nadeau, Philippe
We show that the number of fully packed loop configurations corresponding to a matching with $m$ nested arches is polynomial in $m$ if $m$ is large enough, thus essentially proving two conjectures by...
How can we escape Thomae's relations? (2005)
Krattenthaler, Christian, Rivoal, Tanguy
In 1879, Thomae discussed the relations between two generic hypergeometric $_3F_2$-series with argument 1. It is well-known since then that there are 120 such relations (including the trivial ones...
Trace identities from identities for determinants (2004)
Humphries, Stephen, Krattenthaler, Christian
We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}a_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates. We show that these...
Approximants de Pad\'e des $q$-polylogarithmes (2004)
Krattenthaler, Christian, Rivoal, Tanguy
We solve a Pad\'e-type problem of approximating three specific functions simultaneously by $q$-analogues of polylogarithms, respectively by powers of the logarithm. This problem is intimately related...
Recent progress in the study of representations of integers as sums of squares (2004)
Chan, Heng Huat, Krattenthaler, Christian
In this article, we collect the recent results concerning the representations of integers as sums of an even number of squares that are inspired by conjectures of Kac and Wakimoto. We start with a...
Non-commutative Hopf algebra of formal diffeomorphisms (2004)
Brouder, Christian, Frabetti, Alessandra, Krattenthaler, Christian
The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the...
Non-commutative Hopf algebra of formal diffeomorphisms (2004)
Brouder, Christian, Frabetti, Alessandra, Krattenthaler, Christian
The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the...
Non-commutative Hopf algebra of formal diffeomorphisms (2004)
Brouder, Christian, Frabetti, Alessandra, Krattenthaler, Christian
The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the...
An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series (2003)
Krattenthaler, Christian, Rivoal, Tanguy
We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple integral. This integral generalizes integrals of Vasilenko and Vasilyev...
Descending plane partitions and rhombus tilings of a hexagon with triangular hole (2003)
It is shown that the descending plane partitions of Andrews can be geometrically realized as cyclically symmetric rhombus tilings of a certain hexagon where an equilateral triangle of side length 2...
An Entry of Ramanujan on Hypergeometric Series in his Notebooks (2003)
Rao, K. Srinivasa, Berghe, G. Vanden, Krattenthaler, Christian
Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for $_3F_2(a,a,x;1+a,1+a+N;1)$, where $N$ is a non-negative...
On a hypergeometric identity of Gelfand, Graev and Retakh (2003)
Krattenthaler, Christian, Rosengren, Hjalmar
A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of differential equations, is...
Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers (2003)
Krattenthaler, Christian, Müller, Thomas
We study the number of solutions of the general semigroup equation in one variable, $X^\al=X^\be$, as well as of the system of equations $X^2=X, Y^2=Y, XY=YX$ in $H\wr T_n$, the wreath product of an...
Asymptotics for random walks in alcoves of affine Weyl groups (2003)
Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving...
Some New Formulas for 𝜋 (2003)
Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim
We show how to find series expansions for {\small $\pi$} of the form {\small $\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$}, where {\small $S(n)$} is some polynomial in n (depending on m, p,...
A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system $\tilde A_n$ that was conjectured by Warnaar is given. It makes use of Milne's $A_n$...
Vicious walkers, friendly walkers and Young tableaux III: Between two walls (2002)
Krattenthaler, Christian, Guttmann, Anthony J., Viennot, Xavier G.
We derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls, as well as for the analogous problem for...
Markus Fulmek, Christian Krattenthaler, P. Brändén, A. Claesson, E. Steingrímsson, Catalan Continued Fractions
The bijection given in the paper [1] is the same (modulo the trivial transformation that converts 312-avoiding permutations to 132avoiding permutations, i.e., the transformation which sends every...
On multiplicities of points on Schubert varieties in Graszmannians II (2001)
We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the...
Evaluations of some determinants of matrices related to the Pascal triangle (2001)
We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either...
Some new formulas for $\pi$ (2001)
Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim
We show how to find series expansions for $\pi$ of the form $\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$, where S(n) is some polynomial in $n$ (depending on $m,p,a$). We prove that there...
A determinantal formula for the Hilbert series of one-sided ladder determinantal rings (2001)
Krattenthaler, Christian, Rubey, Martin
We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computation of these Hilbert...
The Hilbert Series of Pfaffian Rings (2001)
Ghorpade, Sudhir R., Krattenthaler, Christian
We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An appendix outlining some...
Enumeration of lozenge tilings of hexagons with cut off corners (2001)
Ciucu, Mihai, Krattenthaler, Christian
Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings...
We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+c,2n+a,2n+b,2n+c$...
On multiplicities of points on Schubert varieties in Grassmannians (2000)
We answer some questions related to multiplicity formulas by Rosenthal and Zelevinsky and by Lakshmibai and Weyman for points on Schubert varieties in Grassmannians. In particular, we give...
Ciucu, Mihai, Krattenthaler, Christian
We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, which gives the number of lozenge tilings of a hexagon with cut off corners. A particularly...
Enumeration of ad-nilpotent $\frak b$-ideals for simple Lie algebras (2000)
Krattenthaler, Christian, Orsina, Luigi, Papi, Paolo
We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.
Vicious walkers, friendly walkers and Young tableaux II: With a wall (2000)
Krattenthaler, Christian, Guttmann, Anthony J., Viennot, Xavier G.
We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory...
Andrews, George E., Krattenthaler, Christian, Orsina, Luigi, Papi, Paolo
We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of $sl(n+1,\Bbb C)$. We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for...
Rectangular Scott-type Permanents (2000)
Han, Guo-Niu, Krattenthaler, Christian
Let $x_1,x_2,...,x_n$ be the zeroes of a polynomial P(x) of degree n and $y_1,y_2,...,y_m$ be the zeroes of another polynomial Q(y) of degree m. Our object of study is the permanent...
Permutations with restricted patterns and Dyck paths (2000)
We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding...
Vicious Walkers, Friendly Walkers and Young Tableaux II: With a Wall (2000)
Tableaux Ii, A Wall, Christian Krattenthaler, Anthony J. Guttmann, Xavier G. Viennot
. We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the...
Enumeration of Lozenge Tilings of Hexagons with Cut Off Corners (2000)
Mihai Ciucu, Christian Krattenthaler
Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings...
Bijections for hook pair identities (1999)
Short, bijective proofs of identities for multisets of `hook pairs' (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.
Fulmek, Markus, Krattenthaler, Christian
We compute the number of rhombus tilings of a hexagon with side lengths N,M,N,N,M,N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The...
Advanced Determinant Calculus (1999)
The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a...
Another involution principle-free bijective proof of Stanley's hook-content formula, preprint (1999)
A bijective proof for Stanley's hook-content formula for the generating function for column-strict reverse plane partitions of a given shape is given that does not involve the involution...
Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets (1999)
Ronald Evans, Henk Hollmann, Christian Krattenthaler, Qing Xiang
We study quadratic residue difference sets, GMW difference sets, and difference sets arising from monomial hyperovals, all of which are (2 d
A New Multidimensional Matrix Inverse With Applications To Multiple q-Series (1999)
Christian Krattenthaler, Michael Schlosser
. We compute the inverse of a specific infinite r-dimensional matrix, extending a matrix inverse of Krattenthaler. Our inversion is different from the r-dimensional matrix inversion recently found by...
Identities for classical group characters of nearly rectangular shape (1998)
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that...
Plane partitions II: 5 1/2 symmetry classes (1998)
Ciucu, Mihai, Krattenthaler, Christian
We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation,...
Another involution principle-free bijective proof of Stanley's hook-content formula (1998)
Another bijective proof of Stanley's hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and...
Gauss Sums, Jacobi Sums, and $p$-ranks of Cyclic Difference Sets (1998)
Evans, Ronald, Hollmann, Henk, Krattenthaler, Christian, Xiang, Qing
We study quadratic residue difference sets, GMW difference sets, and difference sets arising from monomial hyperovals, all of which are $(2^d-1, 2^{d-1}-1, 2^{d-2}-1)$ cyclic difference sets in the...
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten (1998)
Krattenthaler, Christian, Zeilberger, Doron
A determinant evaluation is proven, a special case of which establishes a conjecture of Bombieri, Hunt, and van der Poorten (Experimental Math\. {\bf 4} (1995), 87--96) that arose in the study of...
An involution principle-free bijective proof of Stanley's hook-content formula (1998)
this article is to give a bijective proof for Stanley's hook-content formula [15, Theorem 15.3] for a certain plane partition generating function. In order to be able to state the formula we...
An involution principle-free bijective proof of Stanley's hook-content formula (1998)
this article is to give a bijective proof for Stanley's hook-content formula [15, Theorem 15.3] for a certain plane partition generating function. In order to be able to state the formula we...
Plane Partitions II: 5½ Symmetry Classes (1998)
Mihai Ciucu, Christian Krattenthaler
We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation,...
Fulmek, Markus, Krattenthaler, Christian
We compute the number of rhombus tilings of a hexagon with sides $N,M,N,N,M,N$, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length $M$.
Ciucu, Mihai, Fulmek, Markus, Krattenthaler, Christian
We compute the number of rhombus tilings of a hexagon with sides $N,M,N,N,M,N$, which contain a fixed rhombus on the symmetry axis. A special case solves a problem posed by Jim Propp.
We prove a constant term conjecture of Robbins and Zeilberger (J. Combin. Theory Ser. A 66 (1994), 17-27), by translating the problem into a determinant evaluation problem and evaluating the...
The number of rhombus tilings of a "punctured" hexagon and the minor summation formula (1997)
Okada, Soichi, Krattenthaler, Christian
We compute the number of all rhombus tilings of a hexagon with sides $a,b+1,c,a+1,b,c+1$, of which the central triangle is removed, provided $a,b,c$ have the same parity. The result is a product of...
Schur function identities and the number of perfect matchings of holey Aztec rectangles (1997)
We compute the number of perfect matchings of an $M\times N$ Aztec rectangle where $|N-M|$ vertices have been removed along a line. A particular case solves a problem posed by Propp. Our enumeration...
Asymptotic Redundancies for Universal Quantum Coding (1997)
Krattenthaler, Christian, Slater, Paul B.
Clarke and Barron have recently shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric...
Asymptotic Redundancies for Universal Quantum Coding (1997)
Christian Krattenthaler, Paul Slater
. Clarke and Barron have recently shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a...
Asymptotic Redundancies for Universal Quantum Coding (1996)
Krattenthaler, Christian, Slater, Paul
We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the...
A bijection between Proctor's and Sundaram's odd orthogonal tableaux (1996)
Markus Fulmek, Christian Krattenthaler
Abstract. An explicit bijection between Proctor's odd orthogonal tableaux and Sundaram's odd orthogonal tableaux is given. 1.
Asymptotic redundancies for universal quantum coding (1996)
Christian Krattenthaler, Paul B. Slater
Abstract | Clarke and Barron have recently shown that the Jereys ' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression...
Christian Krattenthaler, A. Sulanke
Abstract. A formula involving a difference of the products of four q-binomial coefficients is shown to count pairs of nonintersecting lattice paths having a prescribed number of weighted turns. The...
A determinant evaluation and some enumeration results for plane partitions (1990)
Abstract. For fixed integers ff and fi, planar arrays of integers of a given shape, in which the entries decrease at least by ff along rows and at least by fi along columns, are considered. The...
Lattice Path Proofs For Determinantal Formulas For Symplectic And Orthogonal Characters
Markus Fulmek, Christian Krattenthaler
. We give bijective proofs for Jacobi--Trudi-type and Giambelli-type identities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkaway's symplectic...
Enumeration of Lozenge Tilings of Hexagons with Cut Off Corners
Mihai Ciucu, Christian Krattenthaler
Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings...
Enumeration Of Ad-Nilpotent B-Ideals For Simple Lie Algebras
Christian Krattenthaler, Luigi Orsina, Paolo Papi
We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having xed class of nilpotence.