We give general lower bounds on the maximal determinant of $n \times 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 $n \bmod 4$, the results 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.
@article{10_37236_2612,
author = {Richard P. Brent and Judy-anne H. Osborn},
title = {General lower bounds on maximal determinants of binary matrices},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/2612},
zbl = {1267.05052},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2612/}
}
TY - JOUR
AU - Richard P. Brent
AU - Judy-anne H. Osborn
TI - General lower bounds on maximal determinants of binary matrices
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2612/
DO - 10.37236/2612
ID - 10_37236_2612
ER -
%0 Journal Article
%A Richard P. Brent
%A Judy-anne H. Osborn
%T General lower bounds on maximal determinants of binary matrices
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2612/
%R 10.37236/2612
%F 10_37236_2612
Richard P. Brent; Judy-anne H. Osborn. General lower bounds on maximal determinants of binary matrices. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/2612
