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https://hdl.handle.net/2142/86907
Description
Title
Minimal Volume K-Point Lattice D-Simplices
Author(s)
Duong, Han
Issue Date
2008
Doctoral Committee Chair(s)
Reznick, Bruce
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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.
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