R. Brent

activity

20072021

most citedOn the stability of the Bareiss and related Toeplitz factorization algorithms

61 citations · 445 across the 59 of their papers we have counts for

collaborators

Showing 2014 · math.COShow all

3 papers · 2 filters

math.CO2014★ 1 cited

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}…

math.CO2014★ 2 cited

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 $r$ and $n$ are…

math.CO2014★ 1 cited

Lower bounds on maximal determinants of binary matrices via the probabilistic method

Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith

Let $D (n)$ be the maximal determinant for $n \times n$ ${\pm 1}$ -matrices, and $R (n) = D (n) / n^{n /2}$ be the ratio of $D (n)$ to the Hadamard upper bound. We give severa…