Conversion of the permanent into the determinant-Reference-Cited by-同舟云学术

Conversion of the permanent into the determinant

Published:1971 Issue:3 Volume:27 Page:471-476
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Gibson P. M.

Abstract

Let A A be an n n -square ( 0 , 1 ) (0,1) -matrix with positive permanent. It is shown that if the permanent of A A can be converted into a determinant by affixing ± \pm signs to the elements of A A then A A has at most ( n 2 + 3 n − 2 ) / 2 ({n^2} + 3n - 2)/2 positive entries. Corollaries of this result are given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-027-03/S0002-9939-1971-0279110-X/S0002-9939-1971-0279110-X.pdf

Reference4 articles.

1. An identity between permanents and determinants;Gibson, P. M.;Amer. Math. Monthly,1969

2. On the relation between the determinant and the permanent;Marcus, Marvin;Illinois J. Math.,1961

3. On lower bounds for permanents of (0,1) matrices;Minc, Henryk;Proc. Amer. Math. Soc.,1969

4. G. Pólya, Aufgabe 424, Arch. Math. Phys. (3) 20 (1913), 271.

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