Quasi-polynomials, linear Diophantine equations and semi-linear sets

Authors:
Flavio DAlessandro;Benedetto Intrigila;Stefano Varricchio
Affiliations:
Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy and Department of Mathematics, Boaziçi University, 34342 Bebek, Istanbul, Turkey;Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 00133 Roma, Italy;Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 00133 Roma, Italy
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We investigate the family of semi-linear sets of N^t and Z^t. We study the growth function of semi-linear sets and we prove that such a function is a piecewise quasi-polynomial on a polyhedral partition of N^t. Moreover, we give a new proof of combinatorial character of a famous theorem by Dahmen and Micchelli on the partition function of a system of Diophantine linear equations.