61 citations · 445 across the 59 of their papers we have counts for
15 papers · 1 filter
Computation of Maximal Determinants of Binary Circulant Matrices
Richard P. Brent, Adam B. Yedidia
We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from …
Discrete analogues of Macdonald-Mehta integrals
Richard P. Brent, Christian Krattenthaler, S. Ole Warnaar
We consider discretisations of the Macdonald--Mehta integrals from the theory of finite reflection groups. For the classical groups, , and $\mathrm…
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}…
Generalising Tuenter's binomial sums
Richard P. Brent
Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form \[S_r(n) = \sum_k \binom{2n}{k}|n-k|^r,\] where and are…
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…