English

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