Abstract: We introduce the Ehrhart theory of algebraic cross-polytopes that undergo vector dilations, generalizing previous work of Borda on scalar dilations of algebraic cross-polytopes and Beck on vector dilations of rational simplices. In particular, for a given class of algebraic cross-polytopes and a dilation vector t dilating each facet, we show that the number of lattice points can be approximated by an explicitly given polynomial of t depending only on the polytope. As a result, we obtain a form of the Ehrhart-Macdonald reciprocity law for the leading term. |
Keywords and phrases: Ehrhart polynomial, vector dilation, irrational polytope, lattice points.
Received: June 20, 2021; Revised: August 23, 2021; Accepted: November 12, 2021; Published: February 16, 2022
How to cite this article: Yashaswika Gaur and Tian An Wong, Lattice points in vector-dilated algebraic polytopes, JP Journal of Algebra, Number Theory and Applications 53(2) (2022), 165-174. DOI: 10.17654/0972555522010
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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