scholarly journals Unconditional Reflexive Polytopes

2020 ◽  
Vol 64 (2) ◽  
pp. 427-452 ◽  
Author(s):  
Florian Kohl ◽  
McCabe Olsen ◽  
Raman Sanyal
Keyword(s):  
Reflexive Polytopes

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 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 Flow polytopes and the graph of reflexive polytopes

2009 ◽  
Vol 309 (16) ◽  
pp. 4992-4999 ◽  
Author(s):  
Klaus Altmann ◽  
Benjamin Nill ◽  
Sabine Schwentner ◽  
Izolda Wiercinska
Keyword(s):  
Flow Polytopes ◽  
Reflexive Polytopes

scholarly journals The Minkowski Property and Reflexivity of Marked Poset Polytopes

10.37236/8144 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Xin Fang ◽  
Ghislain Fourier ◽  
Christoph Pegel
Keyword(s):  
Toric Varieties ◽  
Reflexive Polytopes ◽  
Coordinate Rings

We study the Minkowski property and reflexivity of marked poset polytopes. Both are relevant to the study of toric varieties associated to marked poset polytopes: the Minkowski property can be used to obtain generators of coordinate rings, while reflexive polytopes correspond to Gorenstein–Fano toric varieties.

REFLEXIVE POLYTOPES IN DIMENSION 2 AND CERTAIN RELATIONS IN SL2(ℤ)

2002 ◽  
Vol 01 (02) ◽  
pp. 159-173 ◽  
Author(s):  
LUTZ HILLE ◽  
HARALD SKARKE
Keyword(s):  
Lattice Points ◽  
Lattice Isomorphism ◽  
Two Dimensional ◽  
Winding Number ◽  
Reflexive Polytopes ◽  
Dimension 2

It is well known that there are 16 two-dimensional reflexive polytopes up to lattice isomorphism. One can check directly from the list that the number of lattice points on the boundary of such a polytope plus the number of lattice points on the boundary of the dual polytope is always 12. It turns out that two-dimensional reflexive polytopes correspond to certain relations of two generators A and B of SL 2(ℤ) of length 12. We generalize this correspondence to reflexive configurations with winding number w and relations of length 12w.

scholarly journals The δ-vectors of reflexive polytopes and of the dual polytopes

2016 ◽  
Vol 339 (10) ◽  
pp. 2450-2456 ◽  
Author(s):  
Akiyoshi Tsuchiya
Keyword(s):  
Reflexive Polytopes

scholarly journals Reflexive polytopes arising from edge polytopes

2018 ◽  
Vol 557 ◽  
pp. 438-454
Author(s):  
Takahiro Nagaoka ◽  
Akiyoshi Tsuchiya
Keyword(s):  
Reflexive Polytopes

scholarly journals An Ehrhart Series Formula For Reflexive Polytopes

10.37236/1153 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Benjamin Braun
Keyword(s):  
Ehrhart Polynomial ◽  
Lattice Polytopes ◽  
Reflexive Polytopes ◽  
Ehrhart Series ◽  
Multiplicative Relationship ◽  
Free Sum

It is well known that for $P$ and $Q$ lattice polytopes, the Ehrhart polynomial of $P\times Q$ satisfies $L_{P\times Q}(t)=L_P(t)L_Q(t)$. We show that there is a similar multiplicative relationship between the Ehrhart series for $P$, for $Q$, and for the free sum $P\oplus Q$ that holds when $P$ is reflexive and $Q$ contains $0$ in its interior.

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