Lattice points in vector-dilated quadratic irrational polytopes

2018/10/02 by Gaur, Yashaswika, Wong, Tian An
#11H06 #11P21 #52C07 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.01065

Abstract

We study the Ehrhart theory of quadratic irrational polytopes that undergo vector dilations. That is, for a given polytope with vertices in ℚ(√(D)), and a different dilation factor for each facet, we show that the leading term of the lattice-point count behaves similar to an Ehrhart polynomial, generalizing previous work of Borda on scalar dilations of quadratic irrational polytopes. As a result, a form of the Ehrhart-Macdonald reciprocity law is obtained for the leading term.

Related

• Multidimensional Ehrhart Reciprocity
• A Closer Look at Lattice Points in Rational Simplices
• Counting Lattice Points by means of the Residue Theorem
• Rational polytopes with Ehrhart coefficients of arbitrary period
• New irrational polygons with Ehrhart-theoretic period collapse