Simplicial orders and chordality

被引：7

作者：

Bigdeli, Mina ^{[1
]}

Herzog, Juergen ^{[2
]}

Pour, Ali Akbar Yazdan ^{[1
]}

Zaare-Nahandi, Rashid ^{[1
]}

机构：

[1] IASBS, Dept Math, Zanjan 451951159, Iran

[2] Univ Duisburg Essen, Fachbereich Math, D-45117 Essen, Germany

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2017年 / 45卷 / 04期

关键词：

Chordal clutter; Simplicial order; Betti number; lambda-sequence; Hilbert function;

D O I：

10.1007/s10801-016-0733-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Chordal clutters in the sense of Bigdeli et al. (J Comb Theory Ser A 145: 129-149, 2017) and Morales et al. (Ann Fac Sci Toulouse Ser 6 23(4): 877-891, 2014) are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear resolution appears as the Betti sequence of the circuit ideal of such a chordal clutter. Associated with any simplicial order is a sequence of integers which we call the lambda-sequence of the chordal clutter. All possible lambda-sequences are characterized. They are intimately related to the Hilbert function of a suitable standard graded K-algebra attached to the chordal clutter. By the lambda-sequence of a chordal clutter, we determine other numerical invariants of the circuit ideal, such as the h-vector and the Betti numbers.

引用

页码：1021 / 1039

页数：19

共 14 条

[1] HIGHER CHORDALITY: FROM GRAPHS TO COMPLEXES [J].