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Lattice size in higher dimensions

Abdulrahman Alajmi, Sayok Chakravarty, Zachary Kaplan and Jenya Soprunova

Vol. 17 (2024), No. 1, 153–162
Abstract

The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the context of simplification of the defining equation of an algebraic curve, but appeared implicitly earlier in geometric combinatorics. Previous work on the lattice size was devoted to studying the lattice size in dimensions 2 and 3. We establish explicit formulas for the lattice size of a family of lattice simplices in arbitrary dimension.

Keywords
lattice size, lattice width, lattice polytopes
Mathematical Subject Classification
Primary: 11H06, 52B20, 52C07
Milestones
Received: 9 September 2022
Revised: 23 December 2022
Accepted: 27 December 2022
Published: 15 March 2024

Communicated by Ravi Vakil
Authors
Abdulrahman Alajmi
Department of Mathematics
Public Authority for Applied Education and Training
Ardiya
Kuwait
Sayok Chakravarty
Department of Mathematics, Statistics, and Computer Science
University of Illinois
Chicago, IL
United States
Zachary Kaplan
New Jersey Department of Environmental Protection
Trenton, NJ
United States
Jenya Soprunova
Department of Mathematical Sciences
Kent State University
Kent, OH
United States