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Discrete Polymatroids satisfying a stronger symmetric exchange property (1412.4496v4)

Published 15 Dec 2014 in math.AC

Abstract: In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid satisfies the one-sided strong exchange property, this result provides an alternative proof for one of the main theorems of J. Schweig in \cite{Sc}, where it is shown that every pruned lattice path polymatroid satisfies White's conjecture. In addition, for two classes of pruned lattice path polymatroidal ideals $I$ and their powers we determine their depth and their associated prime ideals, and furthermore determine the least power $k$ for which $\depth S/Ik$ and $\Ass(S/Ik)$ stabilize. It turns out that $\depth S/Ik$ stabilizes precisely when if $\Ass(S/Ik)$ stabilizes.

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