44 citations · 104 across the 13 of their papers we have counts for
13 papers
Probabilistic lower bounds on maximal determinants of binary matrices
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
Let be the maximal determinant for -matrices, and be the ratio of to the Hadam…
Some binomial sums involving absolute values
Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn +1
We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form \[S_{α,β}…
Lower bounds on maximal determinants of binary matrices via the probabilistic method
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
Let be the maximal determinant for -matrices, and be the ratio of to the Hadamard upper bound. We give severa…
Bounds on determinants of perturbed diagonal matrices
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices conside…
Note on a double binomial sum relevant to the Hadamard maximal determinant problem
Richard P. Brent, Judy-anne H. Osborn
We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest becaus…
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…