On the permanent of Sylvester-Hadamard matrices
Combinatorics
2018-02-23 v1
Abstract
We prove a conjecture due to Wanless about the permanent of Hadamard matrices in the particular case of Sylvester-Hadamard matrices. Namely we show that for all n greater or equal to 2, the dyadic valuation of the permanent of the Sylvester-Hadamard matrix of order n is equal to the dyadic valuation of n!. As a consequence, the permanent of the Sylvester-Hadamard matrix of order n doesn't vanish for n greater or equal to 2.
Keywords
Cite
@article{arxiv.1802.08001,
title = {On the permanent of Sylvester-Hadamard matrices},
author = {Ulysse Chabaud},
journal= {arXiv preprint arXiv:1802.08001},
year = {2018}
}
Comments
2 pages