A combinatorial proof of symmetry among minimal star factorizations
Combinatorics
2012-05-22 v2
Abstract
The number of minimal transitive star factorizations of a permutation was shown by Irving and Rattan to depend only on the conjugacy class of the permutation, a surprising result given that the pivot plays a very particular role in such factorizations. Here, we explain this symmetry and provide a bijection between minimal transitive star factorizations of a permutation \pi having pivot k and those having pivot k'.
Keywords
Cite
@article{arxiv.1109.4642,
title = {A combinatorial proof of symmetry among minimal star factorizations},
author = {Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:1109.4642},
year = {2012}
}
Comments
Final version, to appear in Discrete Mathematics