| Matroid Polytopes On the Flow Lattice of Uniform Oriented (2008) | |||||||||||||||||
Abstract | |||||||||||||||||
| Recently Hochstättler and Neˇsetˇril introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. We characterize the flow lattice of a uniform oriented matroid in several ways. One major focus of this work points to the dimension of the lattice. We prove that in the uniform case the dimension is either n or n −1, where the second case exactly belongs to neighborly matroid polytopes of odd rank. Hereby we partially solve a problem stated in Björner et al. [1999]. Furthermore, we construct a basis of the flow lattice consisting of directed circuits. 1 | |||||||||||||||||
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