English

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

R2 v1 2026-06-21T21:51:25.334Z