Upper bounds on the permanent of multidimensional (0,1)-matrices
Combinatorics
2015-03-31 v1
Abstract
The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. By Minc's conjecture, there exists a reachable upper bound on the permanent of 2-dimensional (0,1)-matrices. In this paper we obtain some generalizations of Minc's conjecture to the multidimensional case. For this purpose we prove and compare several bounds on the permanent of multidimensional (0,1)-matrices. Most estimates can be used for matrices with nonnegative bounded entries.
Cite
@article{arxiv.1412.1933,
title = {Upper bounds on the permanent of multidimensional (0,1)-matrices},
author = {A. A. Taranenko},
journal= {arXiv preprint arXiv:1412.1933},
year = {2015}
}