Decomposable clutters and a generalization of Simon's conjectutre

Autor:	Bigdeli, Mina, Pour, Ali Akbar Yazdan, Zaare-Nahandi, Rashid
Rok vydání:	2018
Předmět:	Mathematics - Commutative Algebra Mathematics - Combinatorics Primary 13D02 13F55 Secondary 05E45 05C65
Druh dokumentu:	Working Paper
Popis:	Each (equigenerated) squarefree monomial ideal in the polynomial ring $S=\mathbb{K}[x_1, \ldots, x_n]$ 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 $\langle [n] \rangle$, for all $d$. We then prove this conjecture for $d \geq n-3$. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1807.11012 Zobrazit plný text záznamu View this record from Arxiv