2013/03/18 by Martina Kubitzke, Kubitzke, Martina, Anda Olteanu +1
Computer Science · Mathematics · #13C14 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13F55 #Rings, Modules, and Algebras #Secondary 13C15 #math.AC #math.CO #msc:13C14 #msc:13C15 #msc:13F55
paper · pdf · doi:10.48550/arxiv.1303.4234
6 figures, reference added
openalex publication_date 2013/03/18 · arxiv created 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 from the Luce-decomposable model in algebraic statistics, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial 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 regularity and their Betti numbers.