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The Permanent Rank of a Matrix

โœ Scribed by Yang Yu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
91 KB
Volume
85
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

Define the perrank of a matrix A to be the size of the largest square submatrix of A with nonzero permanent. Motivated in part by the Alon Jaeger Tarsi Conjecture [3], we prove several results on perranks..

๐Ÿ“œ SIMILAR VOLUMES

A matrix of permanents
A matrix of permanents
โœ Ravindra Bapat ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 380 KB
Permanent of the laplacian matrix of tre
Permanent of the laplacian matrix of trees with a given matching
โœ John L Goldwasser ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 715 KB

We define the Laplacian ratio of a tree z(T), to be the permanent of the Laplacian matrix of T divided by the product of the degrees of the vertices. Best possible lower and upper bounds are obtained for ~r(T) in terms of the size of the largest matching in T.