On a valuation of rational subsets ofZk Dédié à Jean Berstel

Authors:
Srecko Brlek;Christophe Reutenauer
Affiliations:
LACIM, Département de Mathématiques et Informatique, UQAM, Montréal, P.Q., Succ. Centre-Ville, Canada H3C 3P8;UFR Mathématiques, Université Louis Pasteur, 7, rue René Descartes, F-67084 Strasbourg, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

A well-known construction associates to each rational subset of Nk a rational function in k commuting variables. We extend this construction to rational subsets of Zk. As a consequence, we derive a multivariate generalization of Popoviciu's theorem and a classical valuation on rational polyhedra.