Betti numbers of chordal graphs and f -vectors of simplicial complexes

JOURNAL OF ALGEBRA

卷:323

Article

Hibi, Takayuki¹  Kimura, Kyouko¹  Murai, Satoshi² 

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Osaka 560043, Japan

[2] Yamaguchi Univ, Fac Sci, Dept Math Sci, Yamaguchi 7538512, Japan

关键词: Monomial ideal;    Betti sequence;    Simplicial complex;    f-Vector;    Chordal graph;   

DOI  :  10.1016/j.jalgebra.2009.12.029

来源: Elsevier

【 摘 要 】

Let G he a chordal graph and I(G) its edge ideal. Let beta(I(G)) = (beta(0), beta(1).....beta(p)) denote the Betti sequence of I(G), where beta(1) stands for the ith total Betti number of I(G) and where p is the projective dimension of I(G). It will be shown that there exists a simplicial complex Delta of dimension p whose f-vector f(Delta) = (f(0). f(1).....f(p)) coincides with beta(I(G)). (C) 2010 Elsevier Inc, All rights reserved.

【 授权许可】

Free