2025/06/04 by Takayuki Hibi, Hibi, Takayuki, S. A. Seyed Fakhari +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2506.03480
openalex publication_date 2025/06/04 · openalex created_date 2025/10/14 · 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∈ℤ>0n, 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. Let I(G) ⊂ S denote the edge ideal of a finite graph G on the vertex set V(G) = \x1, …, xs\. In our previous work, it is shown that (I(G)^δ_\mathfrakc(I))_\mathfrakc is a polymatroidal ideal. Let W(\mathfrakc,G) denote the minimal system of monomial generators of (I(G)^δ_\mathfrakc(I))_\mathfrakc. It follows that W(\mathfrakc,G) satisfies the symmetric exchange property. In the present paper, the question when W(\mathfrakc,G) enjoys the strong exchange property, or equivalently, when W(\mathfrakc,G) is of Veronese type is studied.