Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4596564 | Journal of Pure and Applied Algebra | 2014 | 22 Pages |
Abstract
We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen-Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise in algebraic statistics from the Luce-decomposable model and the ascending model, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial ideals and ascending ideals for diamond posets and products of chains. In particular, for these classes of posets, we explicitly compute their Krull dimension, their projective dimension, their Castelnuovo-Mumford regularity and their Betti numbers.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Martina Kubitzke, Anda Olteanu,