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arXiv:1106.1465 [math.CO]AbstractReferencesReviewsResources

Determinants and Perfect Matchings

Arvind Ayyer

Published 2011-06-07, updated 2012-01-04Version 2

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.

Comments: 15 pages, terminology improved, exposition tightened, "deranged matchings" example removed
Journal: Journal of Combinatorial Theory A 120 (2013) 304-314
Categories: math.CO, cs.DM, math.RA, math.RT
Subjects: 05B20, 05C10, 05C70, 15B57, 15A15
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