Betti numbers and almost complete intersection monomial ideals

2025/05/24 by Амир Мафи, Mafi, Amir, Rando Rasul Qadir +1
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.18788

openalex publication_date 2025/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R=K[x₁,…, x_n] be the polynomial ring in n variables over a field K and let I be a monomial ideal of R. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.

Citations

• Minimal Resolutions of Dominant and Semidominant Ideals
• Almost complete intersections and Stanley's conjecture
• Componentwise linear ideals with minimal or maximal Betti numbers
• Prime filtrations of monomial ideals and polarizations
• Finite Filtrations of Modules and Shellable Multicomplexes
• Powers of complete intersections: graded Betti numbers and applications
• Dirac's theorem on chordal graphs and Alexander duality
• Betti numbers of Zⁿ-graded modules
• Monomial Resolutions

Related

• On the Betti numbers of monomial ideals and their powers
• Monomial ideals with large projective dimension
• Classifying Nearly Complete Intersection Ideals Generated in Degree Two
• Lower Bounds for Betti Numbers of Monomial Ideals
• A note on almost Cohen-Macaulay monomial ideals