Bounds on minors of binary matrices
arXiv:1208.3330 · doi:10.1017/S000497271200086X
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.
9 pages, 1 table. Typo corrected in v2. Two references and Theorem 2 added in v3