Smith normal form in combinatorics

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• 作者：Richard P. Stanley ^{rstan@math.mit.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Smith normal form ; Diagonal form ; Critical group ; Random matrix ; Jacobi&ndash ; Trudi matrix ; Varchenko matrix
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：144
• 期：Complete
• 页码：476-495
• 全文大小：456 K

文摘

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.