Ehrhart quasi-period collapse in rational polygons

2015/09/11 by Tyrrell B. McAllister, McAllister, Tyrrell B., Matthew Moriarity +1
Mathematics · #52B11 #52C07 #Combinatorics (math.CO) #FOS: Mathematics #Primary 52B05 #Secondary 05A15 #math.CO #msc:05A15 #msc:52B05 #msc:52B11 #msc:52C07

paper · pdf · doi:10.48550/arxiv.1509.03680

This article supersedes arXiv:0906.0674

arxiv created 2015/09/11 · arxiv updated 2015/09/15

Abstract

In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of *non*-integral convex polygons. Turning to the case in which the Ehrhart quasi-polynomial has nontrivial quasi-period, we determine the possible minimal periods of the coefficient functions of the Ehrhart quasi-polynomial of a rational polygon.

Citations

• Coefficient functions of the Ehrhart quasi-polynomials of rational polygons

Related

• Coefficient functions of the Ehrhart quasi-polynomials of rational polygons
• Quasi-period collapse in half-integral polygons
• The Minimum Period of the Ehrhart Quasi-polynomial of a Rational Polytope
• Rational polytopes with Ehrhart coefficients of arbitrary period
• New irrational polygons with Ehrhart-theoretic period collapse