VALUES OF THE PERMANENT FUNCTION ON MULTIDIMENSIONAL (0,1)-MATRICES

被引：0

作者：

Guterman, A. E. ^{[1
]}

Evseev, I. M. ^{[2
]}

Taranenko, A. A. ^{[3
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow Inst Phys & Technol, Moscow, Russia

[2] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia

[3] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2022年 / 63卷 / 02期

关键词：

permanent; multidimensional matrix; (0,1)-matrix; Brualdi-Newman theorem;

D O I：

10.1134/S0037446622020057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the range of the permanent function for the multidimensional matrices of 0 and 1. The main result is a multidimensional version for the Brualdi-Newman upper bound on the consecutive values of the permanent (1965). Moreover, we deduce a formula for the permanent of the multidimensional (0,1)-matrices through the number of zero partial diagonals. Using the formula, we evaluate the permanents of the (0, 1)-matrices with a few zeros and estimate the permanents of the matrices whose all zero entries are located in several orthogonal hyperplanes. We consider some divisibility properties of the permanent and illustrate the results by studying the values of the permanent for the 3-dimensional (0, 1)-matrices of order 3.

引用

页码：262 / 276

页数：15

共 50 条

[1] On the values of the permanent of (0,1)-matrices
Guterman, A. E.
Taranin, K. A.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 552 : 256 - 276
[2] A Range of the Multidimensional Permanent on (0,1)-Matrices
Evseev, I. M.
Guterman, A. E.
[J]. SEMIGROUPS, ALGEBRAS AND OPERATOR THEORY, ICSAOT 2022, 2023, 436 : 127 - 147
[3] UPPER BOUNDS ON THE PERMANENT OF MULTIDIMENSIONAL (0,1)-MATRICES
Taranenko, A. A.
[J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2014, 11 : 958 - 965
[4] SOME INEQUALITIES FOR MULTIDIMENSIONAL (0,1)-MATRICES
SCHRAGE, G
[J]. DISCRETE MATHEMATICS, 1978, 23 (02) : 169 - 175
[5] An upper bound for the permanent of (0,1)-matrices
Liang, H
Bai, FS
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 377 : 291 - 295
[6] PERMANENT OF A CERTAIN CLASS OF (0,1)-MATRICES
HARTFIEL, DJ
CROSBY, JW
[J]. CANADIAN MATHEMATICAL BULLETIN, 1971, 14 (04): : 507 - &
[7] On the permanent of certain (0,1) Toeplitz matrices
Codenotti, B
Crespi, V
Resta, G
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 267 : 65 - 100
[8] ASYMPTOTIC NUMBER OF (0,1)-MATRICES WITH ZERO PERMANENT
EVERETT, CJ
STEIN, PR
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A300 - A300
[9] The permanent of 0,1 matrices and Kallman's algorithm
Delic, G
Cash, GG
[J]. COMPUTER PHYSICS COMMUNICATIONS, 2000, 124 (2-3) : 315 - 329
[10] Maximising the permanent and complementary permanent of (0,1)-matrices with constant line sum
Wanless, IM
[J]. DISCRETE MATHEMATICS, 1999, 205 (1-3) : 191 - 205

← 1 2 3 4 5 →