Determinants and Perfect Matchings

Details Determinants and Perfect Matchings Determinants and Perfect Matchings

2011-06-07

arxiv.org/abs/1106.1465v2

Mathematics

Combinatorics

15 pages, terminology improved, exposition tightened, "deranged matchings" example removed

Scientific paper

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.

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