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

A. E. Guterman; K. A. Taranin

doi:https://doi.org/10.1016/j.laa.2018.04.026

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

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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 language	English
Pages (from-to)	256-276
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	552
DOIs	https://doi.org/10.1016/j.laa.2018.04.026
State	Published - 1 Sep 2018
Externally published	Yes

Keywords

(0,1)-matrices
Permanent

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.laa.2018.04.026

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

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.",

keywords = "(0,1)-matrices, Permanent",

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AU - Guterman, A. E.

AU - Taranin, K. A.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

AB - 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.

KW - (0,1)-matrices

KW - Permanent

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U2 - https://doi.org/10.1016/j.laa.2018.04.026

DO - https://doi.org/10.1016/j.laa.2018.04.026

M3 - مقالة

SN - 0024-3795

VL - 552

SP - 256

EP - 276

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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