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A Matrix for Counting Paths in Acyclic Digraphs

✍ Scribed by Richard P. Stanley

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 178 KB
Volume: 74
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0046

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✦ Synopsis

We define a matrix A associated with an acyclic digraph 1, such that the coefficient of z j in det(I+zA) is the number of j-vertex paths in 1. This result is actually a special case of a more general weighted version.

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