General lower bounds on maximal determinants of binary matrices
Combinatorics
2021-07-05 v6 Statistics Theory
Statistics Theory
Abstract
We give general lower bounds on the maximal determinant of n by n {+1,-1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, those of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi's determinant identity, of a result of Sz\"oll\H{o}si (2010) on minors of Hadamard matrices.
Keywords
Cite
@article{arxiv.1208.1805,
title = {General lower bounds on maximal determinants of binary matrices},
author = {Richard P. Brent and Judy-anne H. Osborn},
journal= {arXiv preprint arXiv:1208.1805},
year = {2021}
}
Comments
15 pages, 37 references, 1 table. Typos corrected and theorems renumbered in v6