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

  • D'Alessandro F
  • Intrigila B
  • Varricchio S
  • 2


    Mendeley users who have this article in their library.
  • 4


    Citations of this article.


We investigate the family of semi-linear sets of ℕtand ℤt. 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 ℕt. 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. © 2011 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Linear Diophantine equation
  • Semi-linear set
  • Vector partition function

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Flavio D'Alessandro

  • Benedetto Intrigila

  • Stefano Varricchio

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free