Generating series of the trace group

Authors:
Anne Bouillard;Jean Mairesse
Affiliations:
LIAFA, CNRS, Université Paris 7, Paris Cedex 5, France;LIAFA, CNRS, Université Paris 7, Paris Cedex 5, France
Venue:
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Year:
2003

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Abstract

We prove an analog for trace groups of the Möbius inversion formula for trace monoids (Cartier-Foata, 1969). A by-product is to obtain an explicit and combinatorial formula for the growth series of a trace group. This is used to study the average height of traces.