Minkowski decompositions of associahedra by Carsten Lange

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Signed tree associahedra by Vincent Pilaud

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Arrangements of equal minors in the positive Grassmannian by Miriam Farber, Alexander Postnikov

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One Parameter Composite Semigroups of Linear Bounded Operators in Strong Operator Topology of Schatten Class Cp by Samir Kasim Hassan, Al-Taie M, Al-Malki Anam, Al-Attar Abeer, Mustafa Khaleel Ismael, Fatema Ahmed Sadeq, Radhi A .Zboon, Jehad R.Kider, Samir K .Hassan, Hussain J. M. Alalkawi, Raad H. Majid, Rawaa A. Alomairy, Luma Abdul Ghani Zghair, Hadia Kadhim J.Al-Ogili, Assifa M. Mohamad, Abbas Sheyaa Alwan, Haider L. Aneed, Assim H Yousif, Salema Sultan Salman, Abbas Hussien Miry, Abduladhem A.Ali, Mohammed Zeki Al-Faiz, Sabah N. mahmood, Khansaa Dawood Selman, Shaymaa Tareq Kadhim

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Transitive Packing: A Unifying Concept in Combinatorial Optimization by Schulz, Andreas S., Müller, Rudolf

“…It introduces the notion of transitive packing and the transitive packing polytope. Polytopes that turn out to be special cases of the transitive packing polytope are, among others, the node packing polytope, the acyclic subdigraph polytope, the bipartite subgraph polytope, the planar subgraph polytope, the clique partitioning polytope, the partition polytope, the transitive acyclic subdigraph polytope, the interval order polytope, and the relatively transitive subgraph polytope. …”
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A Polyhedral Intersection Theorem for Capacitated Spanning Trees by Hall, Leslie A., Magnanti, Thomas L.

“…This polytope is the intersection of the spanning tree polytope on the given graph and the matching polytope on the subgraph induced by removing the root node and its incident edges. …”
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Equivariant Semidefinite Lifts and Sum-of-Squares Hierarchies by Fawzi, Hamza, Saunderson, James, Parrilo, Pablo A.

“…A central question in optimization is to maximize (or minimize) a linear function over a given polytope P. To solve such a problem in practice one needs a concise description of the polytope P. …”
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Violation of all two-party facet Bell inequalities by almost-quantum correlations by Ravishankar Ramanathan

“…We also exploit connections between the cut polytope of graph theory and the classical correlation Bell polytope, to show that correlation Bell inequalities that define facets of the lower dimensional correlation polytope are violated in quantum theory.…”
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Contributions to the theory of Ehrhart polynomials by Liu, Fu, Ph. D. Massachusetts Institute of Technology

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Diameters and geodesic properties of generalizations of the associahedron by C. Ceballos, T. Manneville, V. Pilaud, L. Pournin

“…The $n$-dimensional associahedron is a polytope whose vertices correspond to triangulations of a convex $(n + 3)$-gon and whose edges are flips between them. …”
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NONCROSSING SETS AND A GRASSMANN ASSOCIAHEDRON by FRANCISCO SANTOS, CHRISTIAN STUMP, VOLKMAR WELKER

“…On our way we provide general results about order polytopes and their triangulations. We call the simplicial complex the noncrossing complex, and the polytope derived from it the dual Grassmann associahedron. …”
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A Maximum Entropy Approach to the Realizability of Spin Correlation Matrices by Michele Pavon, Paolo Dai Pra, Neeraja Sahasrabudhe

“…Deriving the form of the optimal solution of a maximum entropy problem, we obtain an infinite family of linear inequalities characterizing the polytope of spin correlation matrices. For n ≤ 6, the facet description of such a polytope is provided through a minimal system of Bell-type inequalities.…”
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Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. …”
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Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. …”
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Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. …”
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Cutting plane algorithms for variational inference in graphical models by Sontag, David Alexander

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Geometry of discrete copulas by Perrone, Elisa, Solus, Liam, Uhler, Caroline, Uhler, Caroline

“…We show that the family of ultramodular discrete copulas and its generalization to component-wise convex discrete quasi-copulas also admit representations as polytopes. In doing so, we draw connections to the Birkhoff polytope, the alternating sign matrix polytope, and their generalizations, thereby unifying and extending results on these polytopes from both the statistics and the discrete geometry literature.…”
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Generalized Permutohedra from Probabilistic Graphical Models by Mohammadi, Fatemeh, Uhler, Caroline, Wang, Charles, Yu, Josephine

“…For directed acyclic graphical models and also for mixed graphical models containing undirected, directed, and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. …”
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Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…As α′→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. …”
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A Finite Calculus Approach to Ehrhart Polynomials by Sam, Steven V., Woods, Kevin M.

“…A rational polytope is the convex hull of a finite set of points in R[superscript d] with rational coordinates. …”
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