A study of v-number for some monomial ideals

2023/08/16 by Prativa Biswas, Biswas, Prativa, Mousumi Mandal +1 · 3 citations
Computer Science · Mathematics · #05C38 #05C69 #05E40 #13F20 #13F55 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2308.08604

openalex publication_date 2023/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give formulas for v-number of edge ideals of some graphs like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two cycles and join of two graphs. For an \mathfrakm-primary monomial ideal I⊂ S=K[x₁,…,x_t], we provide an explicit expression of v-number of I, denoted by v(I), and give an upper bound of v(I) in terms of the degree of its generators. We show that for a monomial ideal I, v(Iⁿ⁺¹) is bounded above by a linear polynomial for large n and for certain classes of monomial ideals, the upper bound is achieved for all n≥ 1. For \mathfrak m-primary monomial ideal I we prove that v(I)≤ reg(S/I) and their difference can be arbitrarily large.

Cited by

• v-numbers of integral closure filtrations of monomial ideals
• Comparing the v-number and h-polynomials of edge ideals
• The V-Number of Binomial Edge Ideals: Minimal Cuts and Cycle Graphs

Related

• Some Results on v-Number of Monomial Ideals
• The v-number of Monomial Ideals
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