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ELA

PERMANENTS OF HESSENBERG

(0

,

1)

-MATRICES REVISITED

∗

BRENT J. DESCHAMP† AND BRYAN L. SHADER‡

Abstract. This paper considers the maximum value of the permanent over the classH(m, n) of n×nHessenberg, (0,1)-matrices withm1’s, and shows that among those matrices that attain the maximum value there exists a matrix with a special form. This special form determines the exact value of the maximum permanent onH(m, n) for certain values ofmandn.

Key words. Hessenberg matrices, Permanents.

AMS subject classifications.15A15.

∗Received by the editors January 7, 2008. Accepted for publication on January 13, 2010. Handling

Editor: Shmuel Friedland.

†Department of Mathematics & Statistics, California State Polytechnic University, Pomona,

Pomona, California 91768, USA (bjdeschamp@csupomona.edu).

‡Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071, USA

(bshader@uwyo.edu).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 20-52, January 2010

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