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Dissertation/Thesis Abstract

Minimal volume K-point lattice D-simplices
by Duong, Han, Ph.D., University of Illinois at Urbana-Champaign, 2008, 47; 3337777
Abstract (Summary)

Recently Bey, Henk, and Wills proved that for a polytope [special characters omitted] with k interior lattice points, the volume of P satisfies[special characters omitted]The main focus of this dissertation is to show via triangulations that for d ≥ 3 there is exactly one class (under unimodular equivalence) of nondegenerate lattice simplices in [special characters omitted] with k ≥ 1 interior lattice points and volume [special characters omitted].

We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.

Indexing (document details)
Advisor: Reznick, Bruce
School: University of Illinois at Urbana-Champaign
School Location: United States -- Illinois
Source: DAI-B 69/11, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Lattice points, Simplices, Triangulations, Unimodular transformations
Publication Number: 3337777
ISBN: 978-0-549-91209-5
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