Ayyer, Arvind (2013) Determinants and perfect matchings Journal of Combinatorial Theory, Series A, 120 (1). pp. 304-314. ISSN 0097-3165
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Official URL: https://doi.org/10.1016/j.jcta.2012.08.007
Related URL: http://dx.doi.org/10.1016/j.jcta.2012.08.007
Abstract
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Determinant Expansion; Perfect Matchings; Brauer Diagramsl Pfaffians |
| ID Code: | 140705 |
| Deposited On: | 11 Dec 2025 07:12 |
| Last Modified: | 11 Dec 2025 07:12 |
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