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Brent, Richard P.

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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1323518
Description: 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 (formula presented) obtaining... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1332843
Description: We give upper and lower bounds on the determinant of a small perturbation of the identity matrix. The lower bounds are best possible, and in most cases they are stronger than well-known bounds due to ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1341294
Description: By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Ha... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1040743
Description: 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 simpler. We give severa... More
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Reviewed: Reviewed
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Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1341399
Description: We give general lower bounds on the maximal determinant of n×n {+1,−1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and... More
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Reviewed: Reviewed
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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1331882
Description: Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/nn/2 be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds... More
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Reviewed: Reviewed
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