Expansion of permutations as products of transpositions
Combinatorics
2017-02-21 v1
Abstract
We compute the number of ways a given permutation can be written as a product of exactly transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many particular cases. Along the way we prove several symmetry properties for matrices associated with bipartite graphs, as well as some general (likely known) properties of Young diagrams. The methods involve linear algebra, enumeration of border strip tableau, and a differential operator on symmetric polynomials.
Cite
@article{arxiv.1702.06093,
title = {Expansion of permutations as products of transpositions},
author = {Michael Anshelevich and Matthew Gaikema and Madeline Hansalik and Songyu He and Nathan Mehlhop},
journal= {arXiv preprint arXiv:1702.06093},
year = {2017}
}
Comments
18 pages