Determinants and Perfect Matchings
Combinatorics
2012-08-30 v2 Discrete Mathematics
Rings and Algebras
Representation Theory
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.
Keywords
Cite
@article{arxiv.1106.1465,
title = {Determinants and Perfect Matchings},
author = {Arvind Ayyer},
journal= {arXiv preprint arXiv:1106.1465},
year = {2012}
}
Comments
15 pages, terminology improved, exposition tightened, "deranged matchings" example removed