On the values of the permanent of (0,1)-matrices

A. E. Guterman, K. A. Taranin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we discuss the values of the permanent of (0,1)-matrices of size n. Classical Brualdi–Newman theorem asserts that every integer value from 0 up to 2n−1 can be realized as the permanent of such a matrix. We obtain a result which is at least twice better and in particular we show that all nonnegative integer values which are less than or equal to 2n can be realized. We also investigate the set of integer values that the permanent function cannot attain on the set of (0,1)-matrices.

Original languageEnglish
Pages (from-to)256-276
Number of pages21
JournalLinear Algebra and Its Applications
Volume552
DOIs
StatePublished - 1 Sep 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Funding

The work was financially supported by the grant RSF 17-11-01124.

FundersFunder number
Russian Science Foundation17-11-01124

    Keywords

    • (0,1)-matrices
    • Permanent

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