Timeline for An inequality concerning non-negative integer matrices with constant row and column sums
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Feb 25, 2015 at 18:55 | comment | added | Navin K. | @Suvrit Precisely. | |
| Feb 25, 2015 at 14:16 | comment | added | Suvrit | Just to help me understand: each matrix in $D_{k,M}$ is $M$ times a doubly stochastic matrix, so that in the case mentioned above, if we write $B=N\sum_i \alpha_i P_i$, we have the case of a convex combination of permutation matrices that you allude to in the question, and you are wondering whether for such a $B$, the inequality holds... | |
| Feb 25, 2015 at 12:34 | comment | added | Navin K. | @StefanKohl The inequality I wish to show would prove that the sequence of "degree-$M$ permanents" is sub-multiplicative, which would imply Gurvits's result and also strengthen Vontobel's result by showing that the Bethe permanent is in fact the limit of the sequence of degree-$M$ permanents. | |
| Feb 25, 2015 at 12:30 | comment | added | Navin K. | @StefanKohl This is not so easy for me to answer in comment form. It arises in the context of a certain approximation, called the Bethe approximation, to the permanent of a non-negative square matrix. See arxiv.org/abs/1107.4196 for details on the so-called "Bethe permanent" and its relationship to the permanent. The ArXiv reference shows that the Bethe permanent can be expressed as the limsup of a certain sequence of "degree-$M$ permanents". Gurvits [arxiv.org/abs/1106.2844] has shown that the Bethe permanent is a lower bound on the permanent. (cont'd below) | |
| Feb 25, 2015 at 10:35 | comment | added | მამუკა ჯიბლაძე | Related to the enumeration of pairings between multisets, this answer to the question mathoverflow.net/q/67359/41291 contains a reference | |
| Feb 25, 2015 at 10:21 | comment | added | Stefan Kohl♦ | Where does this question arise? | |
| Feb 25, 2015 at 10:17 | review | First posts | |||
| Feb 25, 2015 at 10:21 | |||||
| Feb 25, 2015 at 10:16 | history | asked | Navin K. | CC BY-SA 3.0 |