A Uniform Asymptotical Upper Bound for the Variance of a Random Polytope in a Simple Polytope by A. Magazinov

“…The present paper contains a sketch of the proof of an upper bound for the variance of the number of hyperfaces of a random polytope when the mother body is a simple polytope. …”
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A Uniform Asymptotical Upper Bound for the Variance of a Random Polytope in a Simple Polytope by A. Magazinov

“…The present paper contains a sketch of the proof of an upper bound for the variance of the number of hyperfaces of a random polytope when the mother body is a simple polytope. …”
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Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves by Ngoc Thinh Nguyen, Pranav Tej Gangavarapu, Niklas Fin Kompe, Georg Schildbach, Floris Ernst

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Mirror Symmetry and Polar Duality of Polytopes by David A. Cox

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On expected number of maximal points in polytopes by Yu. Baryshnikov

Subjects: “…polytope…”
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On Relaxation Polytope of 3-satisfiability Problem by B. V. Uryvaev

“…The properties of a polytope associated with the 3-satisfiability problem are investigated. …”
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Some Properties of Metric Polytope Constraints by V. A. Bondarenko, A. V. Nikolaev

“…The integrality recognition problem is considered on the sequence Mn,k of the nested Boolean quadric polytope relaxations, including the rooted semimetric Mn and the metric Mn,3 polytopes. …”
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Polytopes and $C^1$-convex bodies by Karim Adiprasito, José Alejandro Samper

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Flag enumerations of matroid base polytopes by Sangwook Kim

Subjects: “…matroid base polytopes…”
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The brick polytope of a sorting network by Vincent Pilaud, Francisco Santos

“…The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. …”
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Constructing neighborly polytopes and oriented matroids by Arnau Padrol

Subjects: “…polytope…”
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Generalized associahedra via brick polytopes by Vincent Pilaud, Christian Stump

“…We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. …”
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Confidence polytopes for quantum process tomography by E O Kiktenko, D O Norkin, A K Fedorov

“…In the present work, we propose a generalization of the confidence polytopes approach for quantum state tomography (QST) to the case of quantum process tomography (QPT). …”
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Newton polytope of good symmetric polynomials by Nguyen, Duc-Khanh, Nguyen Thi Ngoc, Giao, Dang Tuan, Hiep, Do Le Hai, Thuy

“…We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. …”
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Certifying quantum separability with adaptive polytopes by Ties-A. Ohst, Xiao-Dong Yu, Otfried Gühne, H. Chau Nguyen

“…We propose a method to certify quantum separability of two- and multiparticle quantum systems based on an adaptive polytope approximation. This leads to an algorithm which, for practical purposes, conclusively recognises two-particle separability for small and medium-size dimensions. …”
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Flow polytopes and the Kostant partition function by Karola Mészáros, Alejandro H. Morales

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Brick polytopes, lattices and Hopf algebras by Vincent Pilaud

“…Moreover, it shows that the fan obtained by coarsening the Coxeter fan according to the classes of ≡k is the normal fan of the corresponding brick polytope…”
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COMPUTING VERTICES OF INTEGER PARTITION POLYTOPES by A. S. Vroublevski, V. A. Shlyk

“…The paper describes a method of generating vertices of the polytopes of integer partitions that was used by the authors to calculate all vertices and support vertices of the partition polytopes for all n ≤ 105 and all knapsack partitions of n ≤ 165. …”
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On a Classification of Smooth Fano Polytopes by Benjamin Assarf, Michael Joswig, Andreas Paffenholz

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Perfect Prismatoids are Lattice Delaunay Polytopes by M. A. Kozachok, A. N. Magazinov

“…The polytope D is a lattice Delaunay polytope if Λ∩int B = ∅ and D is a convex hull of Λ∩∂B. …”
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