An entropy proof of Bergman's theorem
Journal of Combinatorial Theory Series A
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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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 l"p 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