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 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 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.

scholarly journals A combinatorial model for computing volumes of flow polytopes

2019 ◽  
Vol 372 (5) ◽  
pp. 3369-3404 ◽  
Author(s):  
Carolina Benedetti ◽  
Rafael S. González D’León ◽  
Christopher R. H. Hanusa ◽  
Pamela E. Harris ◽  
Apoorva Khare ◽  
...  
Keyword(s):  
Flow Polytopes ◽  
Combinatorial Model

scholarly journals Flow polytopes with Catalan volumes

2017 ◽  
Vol 355 (3) ◽  
pp. 248-259 ◽  
Author(s):  
Sylvie Corteel ◽  
Jang Soo Kim ◽  
Karola Mészáros
Keyword(s):  
Flow Polytopes

scholarly journals Flow Polytopes and the Space of Diagonal Harmonics

2019 ◽  
Vol 71 (6) ◽  
pp. 1495-1521
Author(s):  
Ricky Ini Liu ◽  
Alejandro H. Morales ◽  
Karola Mészáros
Keyword(s):  
Complete Graph ◽  
Hilbert Series ◽  
Threshold Graphs ◽  
Flow Polytopes ◽  
Diagonal Harmonics ◽  
Flow Polytope

AbstractA result of Haglund implies that the$(q,t)$-bigraded Hilbert series of the space of diagonal harmonics is a$(q,t)$-Ehrhart function of the flow polytope of a complete graph with netflow vector$(-n,1,\ldots ,1)$. We study the$(q,t)$-Ehrhart functions of flow polytopes of threshold graphs with arbitrary netflow vectors. Our results generalize previously known specializations of the mentioned bigraded Hilbert series at$t=1$,$0$, and$q^{-1}$. As a corollary to our results, we obtain a proof of a conjecture of Armstrong, Garsia, Haglund, Rhoades, and Sagan about the$(q,q^{-1})$-Ehrhart function of the flow polytope of a complete graph with an arbitrary netflow vector.

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
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