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

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 al...

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Bibliographic Details
Published in:Linear algebra and its applications 2018-09, Vol.552, p.256-276
Main Authors: Guterman, A.E., Taranin, K.A.
Format: Article
Language:English
Subjects:
(0,1)-matrices
Linear algebra
Matrix
Permanent
Sparsity
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.04.026