Stability properties of Plethysm: new approach with combinatorial proofs (Extended abstract) by Laura Colmenarejo

“…We show that these other plethysm coefficients count integer points in polytopes and we prove stability for them by exhibiting bijections between the corresponding sets of integer points of each polytope.…”
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Subword Complexes and Nil-Hecke Moves by M. A. Gorsky

“…We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. …”
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All tight correlation Bell inequalities have quantum violations by Llorenç Escolà, John Calsamiglia, Andreas Winter

“…In geometric terms, this means that any correlation Bell inequality for which the classical and quantum maximum values coincide, does not define a facet, i.e., a face of maximum dimension, of the local (Bell) polytope. Indeed, using semidefinite programming duality, we prove upper bounds on the dimension of these faces, bounding it far away from the maximum. …”
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Algebraic shifting and strongly edge decomposable complexes by Satoshi Murai

“…Kalai and Sarkaria conjectured that if $\Gamma$ is a simplicial sphere then its algebraic shifting also satisfies (c) $\Delta (\Gamma) \subset \Delta (C(n,d))$, where $C(n,d)$ is the boundary complex of the cyclic $d$-polytope with $n$ vertices. We show this conjecture for strongly edge decomposable spheres introduced by Nevo. …”
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Subword Complexes and Nil-Hecke Moves by M. A. Gorsky

“…We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. …”
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Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions by Anatolij N. Kanatnikov, Konstantin E. Starkov

“…The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. …”
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The topology of Baues complexes and flip graphs by Liu, Xue (Mathematician)

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Robust H-infinity filtering of stationary continuous-time linear systems with stochastic uncertainties by Gershon, E, Limebeer, D, Shaked, U, Yaesh, I

“…The method proposed is also applied to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H2/H∞ filtering for the above system is also treated. …”

Approximate counting in SMT and value estimation for probabilistic programs by Chistikov, D, Dimitrova, R, Majumdar, R

“…<p>#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). …”

Higher-order singular value decomposition and the reduced density matrices of three qubits by Choong, Pak Shen, Zainuddin, Hishamuddin, Chan, Kar Tim, Said Husain, Sharifah Kartini

“…Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD.…”
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Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates by Giuseppe Baio, Matthew T. Wheeler, David S. Hall, Janne Ruostekoski, Magnus O. Borgh

“…The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. …”
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Improved local models and new Bell inequalities via Frank-Wolfe algorithms by Sébastien Designolle, Gabriele Iommazzo, Mathieu Besançon, Sebastian Knebel, Patrick Gelß, Sebastian Pokutta

“…We make our entire code accessible as a julia library called BellPolytopes.jl.…”
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Prescriptive unitarity from positive geometries by Livia Ferro, Ross Glew, Tomasz Łukowski, Jonah Stalknecht

“…Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. …”
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The short toric polynomial by Gábor Hetyei

“…This formula implies Gessel's formula for the toric h-vector of a cube, and may be used to prove that the nonnegativity of the toric h-vector of a simple polytope is a consequence of the Generalized Lower Bound Theorem holding for simplicial polytopes.…”
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Universal Polynomials for Severi Degrees of Toric Surfaces by Federico Ardila, Florian Block

“…An important ingredient in the proof is the polynomiality of the discrete volume of a variable facet-unimodular polytope.…”
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The moduli space of Harnack curves in toric surfaces by Jorge Alberto Olarte

“…This compactification has a natural stratification with the same poset as the secondary polytope of $\Delta $.…”
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Positive Configuration Space by Arkani-Hamed, Nima, Lam, Thomas, Spradlin, Marcus

“…This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. …”
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Valid Inequalities and Facets of the Capacitated Plant Location Problem by Leung, Janny M. Y., Magnanti, Thomas L.

“…We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.…”
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A Definition of Type Domain of a Parallelotope by V. P. Grishukhin

“…<p>Each convex polytope P = P(α) can be described by a set of linear inequalities determined by vectors p and right hand sides α(p). …”
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Arnold’s Piecewise Linear Filtrations, Analogues of Stanley–Reisner Rings and Simplicial Newton Polyhedra by Anatoly Kushnirenko

“…Assuming that Newtons polytope is <i>simplicial</i> and <i>super-convenient</i> (that is, containing some neighborhood of the origin), the author strengthens the 1974 result by explicitly specifying the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">B</mi><mrow><mi>s</mi><mi>h</mi></mrow></msup></semantics></math></inline-formula> of monomials of cardinality <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>!…”
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