Geodesic
Upper bounds on the permanent of multidimensional $(0,1)$-matrices
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 958-965

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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.
Mots-clés : permanent, multidimensional matrix, $(0,1)$-matrix. 
@article{SEMR_2014_11_a56,
     author = {A. A. Taranenko},
     title = {Upper bounds on the permanent of multidimensional $(0,1)$-matrices},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {958--965},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a56/}
}
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A. A. Taranenko. Upper bounds on the permanent of multidimensional $(0,1)$-matrices. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 958-965. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a56/