Discrete Polymatroids satisfying a stronger symmetric exchange property
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 $\depth S/I^k$ and $\Ass(S/I^k)$ stabilize. It turns out that $\depth S/I^k$ stabilizes precisely when if $\Ass(S/I^k)$ stabilizes.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2014
- DOI:
- 10.48550/arXiv.1412.4496
- arXiv:
- arXiv:1412.4496
- Bibcode:
- 2014arXiv1412.4496L
- Keywords:
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- Mathematics - Commutative Algebra;
- Primary 13D02;
- 13C13;
- Secondary 05E40
- E-Print:
- 30 to appear in Journal of algebra