scholarly journals Interlacing Ehrhart polynomials of reflexive polytopes

2017 ◽  
Vol 23 (4) ◽  
pp. 2977-2998 ◽  
Author(s):  
Akihiro Higashitani ◽  
Mario Kummer ◽  
Mateusz Michałek
Keyword(s):  
Ehrhart Polynomials ◽  
Reflexive Polytopes

scholarly journals On Counterexamples to a Conjecture of Wills and Ehrhart Polynomials whose Roots have Equal Real Parts

10.37236/3757 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Matthias Henze
Keyword(s):  
Lattice Point ◽  
Convex Bodies ◽  
Discrete Analog ◽  
Side Length ◽  
Ehrhart Polynomials ◽  
Lattice Polytopes ◽  
Lattice Polytope ◽  
Positive Side ◽  
Reflexive Polytopes

As a discrete analog to Minkowski's theorem on convex bodies, Wills conjectured that the Ehrhart coefficients of a $0$-symmetric lattice polytope with exactly one interior lattice point are maximized by those of the cube of side length two. We discuss several counterexamples to this conjecture and, on the positive side, we identify a family of lattice polytopes that fulfill the claimed inequalities. This family is related to the recently introduced class of $l$-reflexive polytopes.

ON FINDING THE COEFFICIENTS d 3 c  OF THE EHRHART POLYNOMIALS OF A POLYHEDRON IN d 

2008 ◽  
Vol 11 (1) ◽  
pp. 105-119
Author(s):  
Shatha Assaad Al-Najjar ◽  
◽  
Manal N. Al-Harere ◽  
Vian A. Al. Al-Salehy ◽  
◽  
...  
Keyword(s):  
Ehrhart Polynomials

scholarly journals Coefficients and roots of Ehrhart polynomials

2005 ◽  
pp. 15-36 ◽  
Author(s):  
M. Beck ◽  
J. A. De Loera ◽  
M. Develin ◽  
J. Pfeifle ◽  
R. P. Stanley
Keyword(s):  
Ehrhart Polynomials

scholarly journals Lattices generated by skeletons of reflexive polytopes

2008 ◽  
Vol 115 (2) ◽  
pp. 340-344 ◽  
Author(s):  
Christian Haase ◽  
Benjamin Nill
Keyword(s):  
Reflexive Polytopes

scholarly journals Ehrhart polynomials of convex polytopes with small volumes

2011 ◽  
Vol 32 (2) ◽  
pp. 226-232 ◽  
Author(s):  
Takayuki Hibi ◽  
Akihiro Higashitani ◽  
Yuuki Nagazawa
Keyword(s):  
Convex Polytopes ◽  
Ehrhart Polynomials

scholarly journals Lower bounds on the coefficients of Ehrhart polynomials

2009 ◽  
Vol 30 (1) ◽  
pp. 70-83 ◽  
Author(s):  
Martin Henk ◽  
Makoto Tagami
Keyword(s):  
Lower Bounds ◽  
Ehrhart Polynomials
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