Bounds on minors of binary matrices
Combinatorics
2013-09-10 v3
Abstract
We prove an upper bound on sums of squares of minors of {+1, -1} matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin (2009), but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices, and generalise a result of Turan on determinants of random {+1,-1} matrices.
Keywords
Cite
@article{arxiv.1208.3330,
title = {Bounds on minors of binary matrices},
author = {Richard P. Brent and Judy-anne H. Osborn},
journal= {arXiv preprint arXiv:1208.3330},
year = {2013}
}
Comments
9 pages, 1 table. Typo corrected in v2. Two references and Theorem 2 added in v3