Values of the Permanent Function on Multidimensional (0,1)-Matrices

A. E. Guterman, I. M. Evseev, A. A. Taranenko

Research output: Contribution to journalArticlepeer-review

Abstract

We study the range of the permanent function for the multidimensional matrices of 0 and 1. The main result is a multidimensional versionfor 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 partial zero diagonals.Using the formula, we evaluate the permanents of the (0,1)-matrices with a few zerosand estimate the permanents of the matrices whose all zero entries are located in several orthogonal hyperplanes.We consider some divisibility properties of the permanent andillustrate the results by studying the values of the permanent for the 3-dimensional (0,1)-matrices of order 3.

Original languageEnglish
Pages (from-to)262-276
Number of pages15
JournalSiberian Mathematical Journal
Volume63
Issue number2
DOIs
StatePublished - Mar 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, Pleiades Publishing, Ltd.

Keywords

  • (0,1)-matrix
  • 512.643:519.142
  • Brualdi–Newman theorem
  • multidimensional matrix
  • permanent

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