Decomposable clutters and a generalization of Simon's conjectutre

2018/07/29 by Mina Bigdeli, Bigdeli, Mina, Ali Akbar Yazdan Pour +3 · 1 citation
Computer Science · Mathematics · #05C65 #13F55 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13D02 #Secondary 05E45

paper · pdf · doi:10.48550/arxiv.1807.11012

openalex publication_date 2018/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Each (equigenerated) squarefree monomial ideal in the polynomial ring S=\mathbbK[x₁, …, x_n] represents a family of subsets of [n], called a (uniform) clutter. In this paper, we introduce a class of uniform clutters, called decomposable clutters, whose associated ideal has linear quotients and hence linear resolution over all fields. We show that chordality of these clutters guarantees the correctness of a conjecture raised by R. S. Simon on extendable shellability of d-skeletons of a simplex ⟨ [n] ⟩, for all d. We then prove this conjecture for d ≥ n-3.

Citations

• Monomial ideals whose powers have a linear resolution

Cited by

• Non-extendably shellable skeleta of simplices

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