Determinants and perfect matchings

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Ayyer, Arvind

关键词: Determinant expansion;    Perfect matchings;    Brauer diagrams;    Pfaffians;   

DOI  :  10.1016/j.jcta.2012.08.007

来源: Elsevier

【 摘 要 】

We give a combinatorial interpretation of the determinant of a matrix as a generating function over Brauer diagrams in two different but related ways. The sign of a permutation associated to its number of inversions in the Leibniz formula for the determinant is replaced by the number of crossings in the Brauer diagram. This interpretation naturally explains why the determinant of an even antisymmetric matrix is the square of a Pfaffian. Published by Elsevier Inc.

【 授权许可】

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