The Canada Day Theorem is an identity involving sums of $k \times k$ minors of an arbitrary $n \times n$ symmetric matrix. It was discovered as a by-product of the work on so-called peakon solutions of an integrable nonlinear partial differential equation proposed by V. Novikov. Here we present another proof of this theorem, which explains the underlying mechanism in terms of the orbits of a certain abelian group action on the set of all $k$-edge matchings of the complete bipartite graph $K_{n,n}$.
@article{10_37236_2449,
author = {Daniel Gomez and Hans Lundmark and Jacek Szmigielski},
title = {The {Canada} day theorem},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2449},
zbl = {1266.15015},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2449/}
}
TY - JOUR
AU - Daniel Gomez
AU - Hans Lundmark
AU - Jacek Szmigielski
TI - The Canada day theorem
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2449/
DO - 10.37236/2449
ID - 10_37236_2449
ER -
%0 Journal Article
%A Daniel Gomez
%A Hans Lundmark
%A Jacek Szmigielski
%T The Canada day theorem
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2449/
%R 10.37236/2449
%F 10_37236_2449
Daniel Gomez; Hans Lundmark; Jacek Szmigielski. The Canada day theorem. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2449
