Classification and Ehrhart Theory of Denominator 2 Polygons

2024/11/28 by Hamm, Girtrude, Hofscheier, Johannes, Kasprzyk, Alexander
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.19183

Abstract

We present an algorithm for growing the denominator r polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small r. We describe the Ehrhart quasi-polynomial of a rational polygon in terms of boundary and interior point counts. Using this, we bound the coefficients of Ehrhart quasi-polynomials of denominator 2 polygons. In particular, we completely classify such polynomials in the case of zero interior points.

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