Hermite normal forms and δ-vectors

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Hibi, Takayuki¹  Higashitani, Akihiro¹  Li, Nan² 

[1] Osaka Univ, Dept Pure & Appl Math, Grad Sch Informat Sci & Technol, Toyonaka, Osaka 5600043, Japan

[2] MIT, Dept Math, Cambridge, MA 02139 USA

关键词: Convex polytope;    Ehrhart polynomial;    delta-Vector;    Hermite normal form;   

DOI  :  10.1016/j.jcta.2012.02.005

来源: Elsevier

【 摘 要 】

Let delta(P) = (delta(0), delta(1), ... , delta(d)) be the delta-vector of an integral polytope P subset of R-N of dimension d. Following previous work on the characterization of delta-vectors with Sigma(d)(i=0) delta(i) <= 3, all the possible delta-vectors with Sigma(d)(i=0) delta(i) = 4 are classified by means of simplices. We obtain our results by considering-by means of Hermite normal forms of square matrices-the classification of integral simplices with a given delta-vector (delta(0), delta(1), ... , delta(d)), where Sigma(d)(i=0) delta(i) <= 4. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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