2017/10/20 by Gunnar Fløystad, Fløystad, Gunnar
Mathematics · #05E40 (Primary) 13C40 #13F55 #14M12 (Secondary) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.CO #msc:05E40 #msc:13C40 #msc:13F55 #msc:14M12
paper · pdf · doi:10.48550/arxiv.1710.07456
29 pages
openalex publication_date 2017/10/20 · arxiv created 2018/04/25 · arxiv updated 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any finite poset P we have the poset of isotone maps Hom(P,ℕ), also called Pop-partitions. To any poset ideal \mathcal J in Hom(P,ℕ), finite or infinite, we associate monomial ideals: the letterplace ideal L(\mathcal J,P) and the Alexander dual co-letterplace ideal L(P,\mathcal J), and study them. We derive a class of monomial ideals in k[xp, p ∈ P] called P-stable. When P is a chain we establish a duality on strongly stable ideals. We study the case when \mathcal J is a principal poset ideal. When P is a chain we construct a new class of determinantal ideals which generalizes ideals of \it maximal minors and whose initial ideals are letterplace ideals of prinicpal poset ideals.