Minors of a skew symmetric matrix: A combinatorial approach
Lars Winther Christensen, Oana Veliche, Jerzy Weyman
TL;DR
This paper revisits a classical formula relating minors of skew symmetric matrices to Pfaffians, using Knuth's combinatorial approach to provide a clearer proof and understanding.
Contribution
It offers a new combinatorial proof of Brill's formula, enhancing clarity and understanding of minors of skew symmetric matrices.
Findings
Reproved Brill's formula using combinatorial methods
Clarified the relationship between minors and Pfaffians
Provided insights into the structure of skew symmetric matrices
Abstract
We use Knuth's combinatorial approach to Pfaffians to reprove and clarify a century-old formula, due to Brill. It expresses arbitrary minors of a skew symmetric matrix in terms of Pfaffians.
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