2025/04/30 by Takayuki Hibi, Hibi, Takayuki, S. A. Seyed Fakhari +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2504.21760
openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S=K[x1, …,xn] denote the polynomial ring in n variables over a field K and I ⊂ S a monomial ideal. Given a vector \mathfrakc∈ℕn, the ideal I_\mathfrakc is the ideal generated by those monomials belonging to I whose exponent vectors are componentwise bounded above by \mathfrakc. Let δ_\mathfrakc(I) be the largest integer q for which (Iq)_\mathfrakc≠ 0. For a finite graph G, its edge ideal is denoted by I(G). Let B(\mathfrakc,G) be the toric ring which is generated by the monomials belonging to the minimal system of monomial generators of (I(G)^δ_\mathfrakc(I))_\mathfrakc. In a previous work, the authors proved that (I(G)^δ_\mathfrakc(I))_\mathfrakc is a polymatroidal ideal. It follows that B(\mathfrakc,G) is a normal Cohen--Macaulay domain. In this paper, we study the Gorenstein property of B(\mathfrakc,G).