An upper bound for permanents of nonnegative matrices

Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Pages (from-to)279-292
Number of pages14
JournalJournal of Combinatorial Theory. Series A
Volume115
Issue number2
DOIs
StatePublished - Feb 2008
Externally publishedYes

Keywords

  • Bounds and approximation algorithms for the permanent

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