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Determinants and Möbius functions in trace monoids

✍ Scribed by Christian Choffrut; Massimiliano Goldwurm

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 430 KB
Volume: 194
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00211-8

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✦ Synopsis

We show that the independence relation defining a trace monoid M admits a transitive orientation if and only if the characteristic series ~ of a lexicographic cross section of M is the inverse of the determinant of (Id-X), where X is a matrix representing the minimum finite automaton recognizing ~ and Id is the identity matrix. This implies that, if the independence relation of a trace monoid M admits a transitive orientation, then any unambiguous lifting of the M6bius function of M is the determinant of a matrix defined by the smallest acceptor of the corresponding cross section. (~

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