2022/12/19 by Gunnar Fløystad, Fløystad, Gunnar, Gabrielsen, Ine +1
Computer Science · Mathematics · #05E45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 13F55 #Secondary: 05E40 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2212.09528
openalex publication_date 2022/12/19 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
We show that any polarization of an Artin monomial ideal defines a triangulated ball. This proves a conjecture of A.Almousa, H.Lohne and the first author. Geometrically, polarizations of ideals containing (x1a1, …, xnan) define full-dimensional triangulated balls on the sphere which is the join of boundaries of simplices of dimensions a1-1, ⋯, an-1. We prove that every full-dimensional Cohen-Macaulay sub-complex of this joined sphere is of this kind, and these balls are constructible. Such a triangulated ball has a dual cell complex which is a sub-complex of the product of simplices of dimensions a1-1, ⋯ an-1. We prove that this cell complex gives cellular minimal free resolution of this of the Alexander dual ideal of the triangulated ball. When the product of simplices is a hypercube, using these dual cell complexes we classify in a range examples all polarizations of the Artin monomial ideal. We also show that the squeezed balls of G.Kalai \citeKa derive from polarizations of Artin monomial ideals.