| Regular sequences of symmetric polynomials (2008) | |||||||||
Abstract | |||||||||
| 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 sums in n variables form a regular sequence. We consider then the following problem: describe the subsets n powersums forming a regular sequence. A necessary condition is that n! divides the product of the degrees of the elements. To find an easily verifiable sufficient condition turns out to be surprisingly difficult already in 3 variables. Given positive integers a. Comment: Minors changes, references added, to appear in Rendiconti del Seminario Matematico della Universita' di Padova | |||||||||
Details der Publikation | |||||||||
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