Smooth polytopes with negative Ehrhart coefficients

Federico Castillo, Fu Liu, Benjamin Nill, Andreas Paffenholz

Type: Article

Publication Date: 2018-07-24

Citations: 8

DOI: https://doi.org/10.1016/j.jcta.2018.06.014

View Publication

Download PDF

Locations

Journal of Combinatorial Theory Series A - View - PDF
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Smooth polytopes with negative Ehrhart coefficients	2017	Federico Castillo Fu Liu Benjamin Nill Andreas Paffenholz
+	Smooth polytopes with negative Ehrhart coefficients	2017	Federico Castillo Fu Liu Benjamin Nill Andreas Paffenholz
+ PDF Chat	On Positivity of Ehrhart Polynomials	2019	Fu Liu
+	Erratum: The Ehrhart Polynomial of a Lattice Polytope	1997	Ricardo Diaz Sinai Robins
+	On positivity of Ehrhart polynomials	2017	Fu Liu
+	The Characterisation Problem of Ehrhart Polynomials of Lattice Polytopes	2022	Akihiro Higashitani
+	Counting Lattice Points in Polytopes:The Ehrhart Theory	2007
+	Lattice polytopes, Hecke operators, and the Ehrhart polynomial	2004	Paul E. Gunnells Fernando Rodríguez Villegas
+ PDF Chat	Notes on the Roots of Ehrhart Polynomials	2007	Christian Bey Martin Henk Jörg M. Wills
+	Rational Ehrhart Theory	2021	Matthias Beck Sophia Elia Sophie Rehberg
+	Rational Ehrhart Theory	2021	Matthias Beck Sophia Elia Sophie Rehberg
+ PDF Chat	Lattice polytopes, Hecke operators, and the Ehrhart polynomial	2007	Paul E. Gunnells Fernando Rodríguez Villegas
+	An Ehrhart polynomial for a dual polytope and the number of lattice points	2014	Iosr Journals Israa H. Hassan Dr. Shatha A. Salman Al-Najjar
+	Notes on the roots of Ehrhart polynomials	2006	Christian Bey Martin Henk J. M. Wills
+	Thin polytopes: Lattice polytopes with vanishing local $h^*$-polynomial	2022	Christopher Borger A. Kretschmer Benjamin Nill
+	On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity	2018	Fu Liu Liam Solus
+	Unimodality Problems in Ehrhart Theory	2015	Benjamin Braun
+	Lattice-points enumeration in polytopes: study of the coefficients of the Ehrhart quasi-polynomial	2016	Hélène O. Rochais
+ PDF Chat	Unimodality problems in Ehrhart theory	2016	Benjamin Braun
+ PDF Chat	Ehrhart Polynomial Roots of Reflexive Polytopes	2019	Gábor Hegedüs Akihiro Higashitani Alexander Kasprzyk

Works That Cite This (8)

Action	Title	Year	Authors
+	Stanley's non-Ehrhart-positive order polytopes	2019	Fu Liu Akiyoshi Tsuchiya
+	On algebraic properties of matroid polytopes	2020	Michał Lasoń Mateusz Michałek
+ PDF Chat	On the Todd class of the permutohedral variety	2021	Federico Castillo Fu Liu
+ PDF Chat	Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity	2022	Katharina Jochemko Mohan Ravichandran
+ PDF Chat	On Positivity of Ehrhart Polynomials	2019	Fu Liu
+ PDF Chat	Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP	2019	Matthias Beck Christian Haase Akihiro Higashitani Johannes Hofscheier Katharina Jochemko Lukas Katthän Mateusz Michałek
+ PDF Chat	On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity	2019	Fu Liu Liam Solus
+	On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity	2018	Fu Liu Liam Solus

Works Cited by This (13)

Action	Title	Year	Authors
+	Commutative Algebra and Algebraic Geometry	1982	Masayoshi Nagata
+	Enumerative Combinatorics: Volume 1	2011	Richard P. Stanley
+	An algorithm for the classification of smooth Fano polytopes	2007	Mikkel Øbro
+	The quest for counterexamples in toric geometry	2011	Winfried Bruns
+ PDF Chat	Local Euler–Maclaurin Formula for Polytopes	2007	Nicole Berline Michèle Vergne
+ PDF Chat	A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron	2002	Richard P. Stanley Jim Pitman
+ PDF Chat	Permutohedra, Associahedra, and Beyond	2009	Alexander Postnikov
+	Higher integrality conditions, volumes and Ehrhart polynomials	2010	Fu Liu
+	Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes	1977	Peter McMullen
+	Berline-Vergne valuation and generalized permutohedra	2015	Federico Castillo Fu Liu