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

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

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

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Authors

  • Flavio D'Alessandro

  • Benedetto Intrigila

  • Stefano Varricchio

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