Smith normal form in combinatorics

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:144

Article

Stanley, Richard P.¹ 

[1] Univ Miami, Dept Math, Coral Gables, FL 33124 USA

关键词: Smith normal form;    Diagonal form;    Critical group;    Random matrix;    Jacobi-Trudi matrix;    Varchenko matrix;   

DOI  :  10.1016/j.jcta.2016.06.013

来源: Elsevier

【 摘 要 】

This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith normal form of random integer matrices. We then give some examples of Smith normal form and diagonal form arising from (1) symmetric functions, (2) a result of Carlitz, Roselle, and Scoville, and (3) the Varchenko matrix of a hyperplane arrangement. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free