Smooth polytopes with negative Ehrhart coefficients

Brown, André EX (5398142); Ch'ng, Quee-Lim (5398154); Currie, Michael (5398160); Grundy, Laura J (5398148); Hokanson, Jim (5398172); Javer, Avelino (5398151); Kerr, Rex (5398163); Lee, Chee Wai (5398145); Li, Chris (5398175); Li, Kezhi (5398157); Schafer, William R (5398166); Yemini, Eviatar (5398169)

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Smooth polytopes with negative Ehrhart coefficients

Authors: André EX (5398142) Brown
Quee-Lim (5398154) Ch'ng
Michael (5398160) Currie
Laura J (5398148) Grundy
Jim (5398172) Hokanson
Avelino (5398151) Javer
Rex (5398163) Kerr
Chee Wai (5398145) Lee
Chris (5398175) Li
Kezhi (5398157) Li
William R (5398166) Schafer
Eviatar (5398169) Yemini
Publication date: 19 June 2018
Publisher
Doi

Abstract

We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative. This answers a question by Bruns. We also discuss Berline-Vergne valuations as a useful tool in proving Ehrhart positivity results.Comment: 15 pages, 1 figure, 1 table, accepted by Journal of Combinatorial Theory Ser.

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Last time updated on 13/08/2018