On Partition Dimension of Generalized Convex Polytopes by Syed Waqas Shah, Muhammad Yasin Khan, Gohar Ali, Irfan Nurhidayat, Soubhagya Kumar Sahoo, Homan Emadifar

“…In this work, we consider convex polytopes in their generalized forms that are En,Sn, and Gn, and we compute upper bounds for the partition dimension of the desired polytopes.…”
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Ehrhart Polynomials of a Cyclic Polytopes by Shatha Assaad Salman, Fatema Ahmed Sadeq

Subjects: “…cyclic polytopes…”
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The Maximal Number of Vertices of The Reflexive Polytope by Shatha A.Salman, Noor Rashid Shabeeb

“…Finally techniques are used to prove the conjecture |V(P)|≤6^(d/2) of the maximal number of vertices for a simplicialreflexive polytopes of even dimension.…”
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Approximate cone factorizations and lifts of polytopes by Gouveia, Joao, Parrilo, Pablo A., Thomas, Rekha R.

“…In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. …”
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Chain Polytopes and Algebras with Straightening Laws by Hibi, Takayuki, Li, Nan

“…It will be shown that the toric ring of the chain polytope of a finite partially ordered set is an algebra with straightening laws on a finite distributive lattice. …”
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Linear Encodings for Polytope Containment Problems by Sadraddini, Sadra, Tedrake, Russell L

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Extension complexity of low-dimensional polytopes by Kwan, Matthew, Sauermann, Lisa, Zhao, Yufei

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Root polytopes, triangulations, and subdivision algebras by Mészáros, Karola

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Polyhedral Gauss sums, and polytopes with symmetry by Malikiosis, Romanos-Diogenes, Robins, Sinai, Zhang, Yichi

“…We define certain natural finite sums of nn'th roots of unity, called GP(n)GP(n), that are associated to each convex integer polytope PP, and which generalize the classical 11-dimensional Gauss sum G(n)G(n) defined over Z/nZZ/nZ, to higher dimensional abelian groups and integer polytopes. …”
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The inverse moment problem for convex polytopes by Gravin, Nick., Lasserre, Jean., Pasechnik, Dmitrii V., Robins, Sinai.

“…We present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, assuming knowledge of finitely many of its integral moments. …”
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Einstein equations, superpotentials and convex polytopes by Dancer, A, Wang, M

Zero-patterns of polynomials and Newton polytopes by Lauder, A

“…The bound is related to the number of lattice points in the Newton polytopes of the polynomials, and is optimal to within a factor depending only on the dimension (assuming suitable inequalities hold amongst the relevant parameters). …”

The inverse moment problem for convex polytopes by Gravin, N, Lasserre, J, Pasechnik, D, Robins, S

From cracked polytopes to Fano threefolds by Prince, T

“…We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes—polytopes whose intersection with a complete fan forms a set of unimodular polytopes—using Laurent inversion; a method developed jointly with Coates–Kasprzyk. …”

The inverse moment problem for convex polytopes by Gravin, N, Lasserre, J, Pasechnik, D, Robins, S

“…The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. …”

A note on polytopes for scattering amplitudes by Arkani-Hamed, N, Bourjaily, J, Cachazo, F, Hodges, A, Trnka, J

Linear Programming, the Simplex Algorithm and Simple Polytopes by Das Bhusan, Biswal Bagaban, J.P Tripathy

Subjects: “…Randomized Pivot rule complexity combinational theory of simple polytopes…”
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Covering cross-polytopes with smaller homothetic copies by Feifei Chen, Shenghua Gao, Senlin Wu

“…Let $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $. …”
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More About the Height of Faces in 3-Polytopes by Borodin Oleg V., Bykov Mikhail A., Ivanova Anna O.

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Quantum Walk on the Generalized Birkhoff Polytope Graph by Rafael Cação, Lucas Cortez, Ismael de Farias, Ernee Kozyreff, Jalil Khatibi Moqadam, Renato Portugal

Subjects: “…generalized Birkhoff polytope…”
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