An upper bound for permanents of nonnegative matrices |
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Authors: | Alex Samorodnitsky |
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Institution: | School of Computer Science and Engineering, Hebrew University, Jerusalem, Israel |
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Abstract: | 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. |
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Keywords: | Bounds and approximation algorithms for the permanent |
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