General lower bounds on maximal determinants of binary matrices
arXiv:1208.1805 · doi:10.37236/2612
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 Szöllősi (2010) on minors of Hadamard matrices.
15 pages, 37 references, 1 table. Typos corrected and theorems renumbered in v6