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

doi:10.1016/j.tcs.2011.10.014

Theoretical Computer Science

Volume 416, 27 January 2012, Pages 1-16

https://doi.org/10.1016/j.tcs.2011.10.014 Get rights and content

Under an Elsevier user license

open archive

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.

Keywords

Semi-linear set

Linear Diophantine equation

Vector partition function

Cited by (0)

^☆: This work was partially supported by MIUR project “Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali”. The first author also acknowledges the partial support of fundings “Facoltà di Scienze MM. FF. NN. 2008” of the University of Rome “La Sapienza”.

¹: Stefano Varricchio suddenly passed away on August 20th 2008. At that moment, many topics of the present paper had been discussed at length with him. So we want to include his name as an author of this work. Stefano Varricchio was a best friend of both of us. For a scientific and personal memory, see D’Alessandro and A. de Luca (2008) [8].

Theoretical Computer Science

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

Abstract

Keywords