From superintegrability to tridiagonal representation of β-ensembles by A. Mironov, A. Morozov, A. Popolitov

“…These potentially useful formulas are usually deduced from rather complicated and non-transparent combinatorics and are not as widely known as they deserve. …”
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Pauli channels can be estimated from syndrome measurements in quantum error correction by Thomas Wagner, Hermann Kampermann, Dagmar Bruß, Martin Kliesch

“…Our proof combines Boolean Fourier analysis, combinatorics and elementary algebraic geometry. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.…”
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Creativity – process, person, and product: Review of some discoveries on creativity in the last decade by Martina Opaka

“…The third viewpoint of creativity – the viewpoint of a creative product – uses analysis of real creative achievement and discoveries of the former two viewpoints to explain creativity as a stochastic process far more dependent on combinatorics, probability and luck than assumed before.…”
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Another look at HMAC by Koblitz Neal, Menezes Alfred

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The topological symmetric orbifold by Songyuan Li, Jan Troost

“…Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly. …”
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Принципи на изследването на формалните класове при глаголните лексеми в съвременния български книжовен език... by Руска [Ruska] Станчева [Stancheva]

“…The fundamental criterion is the combinatorics of the values of three types of thematic grammemes (praesens, aoristi and imperfectum). …”
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The Edit Distance Function of Some Graphs by Hu Yumei, Shi Yongtang, Wei Yarong

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ON THE STRUCTURE OF GRAPHS WHICH ARE LOCALLY INDISTINGUISHABLE FROM A LATTICE by ITAI BENJAMINI, DAVID ELLIS

“…Our proofs use a mixture of techniques and results from combinatorics, geometry and group theory.…”
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Method of an Analysis of the Nonlinear Monotonic Simultaneous Stability of Two Orientation Angles of an Asymmetric Spacecraft in the Martian Atmosphere by Vladislav V. Lyubimov

“…The method is based on the application of the classical mathematical investigation method for the function of one independent variable and combinatorics. The method assumes that two analyzed functions describing the evolution of two orientation angles are defined and are twice continuously differentiable over the considered interval of change of the independent variable. …”
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Generalized matrix functions, determinant and permanent by Mohammad Hossein Jafari, Ali Reza Madadi

“…Generalized matrix functions connect some branches of mathematics such as theory of finite groups, representation theory of groups, graph theory and combinatorics, and linear and multilinear algebra.    …”
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Imagological Paradigm of Serbian Novel of the First Half of the 20 th Century by Natalia Bilyk

“…In the dynamics of imagological image there is a dominance of variability from the focus of poetics on the phenomenon of classical oppositions I/Other, My/Strange to the change of combinatorics to the binary relationship I/Stranger and My/My-as-Strange. …”
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The Systems Measurement of Mammalian Biotas, Part Two by Charles H. Smith, Patrick Georges, Ngoc Nguyen

“…An additional analysis of the same mode is described here, in which the seven-region model of the distribution of mammal families’ spatial affinities is shown to closely approach a most-probable-state arrangement, as assessed through combinatorics, raising some important questions about how macroevolutionary patterns might self-organize spatially. …”
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Robust online Hamiltonian learning by Christopher E Granade, Christopher Ferrie, Nathan Wiebe, D G Cory

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Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] by Venkateswaran, Vidya

“…In both cases, the technique involves combinatorics of the Gelfand-Tsetlin bases. As an application, we obtain information about unitarity of finite-dimensional irreducible representations for arbitrary q: we classify the continuous spectrum of the unitarity locus. …”
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Exact formulae for the fractional partition functions by Iskander, Jonas, Jain, Vanshika, Talvola, Victoria

“…Abstract The partition function p(n) has been a testing ground for applications of analytic number theory to combinatorics. In particular, Hardy and Ramanujan invented the “circle method” to estimate the size of p(n), which was later perfected by Rademacher who obtained an exact formula. …”
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Geometry of Log-Concave Density Estimation by Robeva, Elina, Sturmfels, Bernd, Uhler, Caroline

“…This article establishes a new link between geometric combinatorics and nonparametric statistics, and it suggests numerous open problems.…”
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Explicit Construction of RIP Matrices Is Ramsey‐Hard by Gamarnik, David

“…In this short note we resolve this open question by showing that an explicit construction of a matrix satisfying the RIP in the regime n = O(log2p) and s = Θ(n1/2) implies an explicit construction of a three-colored Ramsey graph on p nodes with clique sizes bounded by O(log2p) — a question in the field of extremal combinatorics that has been open for decades. © 2019 Wiley Periodicals, Inc.…”
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Intersection Graphs of Maximal Sub-polygons of k-Lizards by Daugherty, Caroline, Laison, Joshua D., Robinson, Rebecca, Salois, Kyle

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A cluster of results on amplituhedron tiles by Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Sherman-Bennett, Melissa, Tessler, Ran, Williams, Lauren

“…It generalizes cyclic polytopes and the positive Grassmannian and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the 𝑚=4 amplituhedron. …”
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Parallel Computation of the Minimal Elements of a Poset by Leiserson, Charles E., Maza, Marc Moreno, Li, Liyun, Xie, Yuzhen

“…Computing the minimal elements of a partially ordered finite set (poset) is a fundamental problem in combinatorics with numerous applications such as polynomial expression optimization, transversal hypergraph generation and redundant component removal, to name a few. …”
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