TY - JOUR

T1 - An upper bound for permanents of nonnegative matrices

AU - Samorodnitsky, Alex

PY - 2008/2

Y1 - 2008/2

N2 - A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in lp is attained either for the identity matrix I or for a constant multiple of the all-1 matrix J. The conjecture is known to be true for p = 1 (I) and for p ≥ 2 (J). We prove the conjecture for a subinterval of (1, 2), and show the conjectured upper bound to be true within a subexponential factor (in the dimension) for all 1 < p < 2. In fact, for p bounded away from 1, the conjectured upper bound is true within a constant factor.

AB - A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in lp is attained either for the identity matrix I or for a constant multiple of the all-1 matrix J. The conjecture is known to be true for p = 1 (I) and for p ≥ 2 (J). We prove the conjecture for a subinterval of (1, 2), and show the conjectured upper bound to be true within a subexponential factor (in the dimension) for all 1 < p < 2. In fact, for p bounded away from 1, the conjectured upper bound is true within a constant factor.

KW - Bounds and approximation algorithms for the permanent

UR - http://www.scopus.com/inward/record.url?scp=41749096792&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2007.05.010

DO - 10.1016/j.jcta.2007.05.010

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AN - SCOPUS:41749096792

SN - 0097-3165

VL - 115

SP - 279

EP - 292

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 2

ER -