44 citations · 104 across the 13 of their papers we have counts for
4 papers · 1 filter
Lower bounds on maximal determinants of +-1 matrices via the probabilistic method
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
We show that the maximal determinant D(n) for -matrices satisfies . Here is the Hadamard upper bound, and de…
Bounds on minors of binary matrices
Richard P. Brent, Judy-anne H. Osborn
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 si…
On minors of maximal determinant matrices
Richard P. Brent, Judy-anne H. Osborn
By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrices of order m > n/2. We generalise this result to maximal determinant submatrices of H…
General lower bounds on maximal determinants of binary matrices
Richard P. Brent, Judy-anne H. Osborn
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 r…