Chromatic roots as algebraic integers by Adam Bohn

“…At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the ``$α +n$ conjecture'' and the ``$nα$ conjecture''. …”
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On the Erdős-Gyárfás Conjecture in Claw-Free Graphs by Nowbandegani Pouria Salehi, Esfandiari Hossein, Haghighi Mohammad Hassan Shirdareh, Bibak Khodakhast

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Poset binomials and rainbow characters by Daniel Bragg, Nathaniel Thiem

“…These coefficients arise naturally in the study of supercharacters of the finite groups of unipotent upper-triangular matrices, whose representation theory is dictated by the combinatorics of set partitions. In particular, we find a natural set of modules for these groups, whose characters have degrees given by $q$-binomials, and whose decomposition in terms of supercharacters are given by poset binomial coefficients. …”
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Seven Études on dynamical Keldysh model by Dmitri V. Efremov, Mikhail N. Kiselev

“…Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. …”
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Two New Classes of Codebooks Asymptotically Achieving the Welch Bound by Shimin Sun, Li Han, Yang Yan, Yao Yao

“…Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and prove that these codebooks asymptotically achieve the Welch bound. …”
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Workflow Modelling and Analysis Based on the Construction of Task Models by Glória Cravo

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OPTIMAL IDENTIFICATION OF RANDOM EVENTS by Boris N. Chugaev, Alexander Y. Arzhenenko

“…Theory questionnaires - a branch of mathematics that arose at the turn of mathematical statistics, combinatorics, graph theory and information theory. Its founder K.F.Pikar developed this theory as a description of the device logical relationships of tasks and methods of their solutions and the conditions under which these decisions are made. …”
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A bound for Dickson's lemma by Josef Berger, Helmut Schwichtenberg

“…By a combinatorial argument (due to the first author) a simple bound for such $i,j$ is constructed. The combinatorics is based on the finite pigeon hole principle and results in a descent lemma. …”
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A new class of generalized polynomials associated with Milne-Thomson-based poly-Bernoulli polynomials by Waseem Ahmad Khan, Divesh Srivastava, Kottakkaran Sooppy Nisar

“…Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other field of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. …”
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A direct computation of a certain family of integrals by Lorenzo Fornari, Enrico Laeng, Vittorino Pata

“…Design/methodology/approach – Combinatorics, sine and cosine integral functions. Findings – The authors prove an explicit formula to evaluate sinc-type integrals. …”
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Non-adaptive Group Testing on Graphs by Hamid Kameli

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Graph dominance by rook domains for Znp and Zn3 × Zm2 graphs by Eduardo Piza Volio

“…Keywords: Graph domination, simulated annealing, football pool problem, combinatorics.…”
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Frequency-Hopping Sequences With Optimal Average Hamming Correlation and Their Applications in Energy and Spectrum Harvesting Technologies Area by Mingyue Fan

“…The research of cyclotomy theory can be traced to Gauss and it has been applied to many fields such as cryptography, coding theory, and combinatorics. According to <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula> prime numbers or compound words, the incision on the residue-like ring <inline-formula> <tex-math notation="LaTeX">${\mathbb Z}_{v}$ </tex-math></inline-formula> can be separated to classic incision or general incision. …”
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Witness structures and immediate snapshot complexes by Dmitry N. Kozlov

“…These objects are indexing the simplices in the immediate snapshot complexes, while a special operation on them, called ghosting, describes the combinatorics of taking simplicial boundary. In general, we develop the theory of witness structures and use it to prove several combinatorial as well as topological properties of the immediate snapshot complexes.…”
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A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems by Seonghyuk Im, Jaehoon Kim, Joonkyung Lee, Abhishek Methuku

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Problems for combinatorial numbers satisfying a class of triangular arrays by Igoris Belovas

“…In this work, we derive the general analytic expression of the numbers satisfying a class of triangular arrays and propose problems (both teaching and unsolved ones) for undergraduates studying probability theory and analytical combinatorics subjects in the study programs of the fields of mathematics and computer science. …”
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From the Earth to the World. Ai Weiwei's Functional Dante Reference in the Music Album <i>The Divine Comedy</i> (2013) and in the Lego Portrait <i>Dante Alighieri in LEGO</i> (2016... by Daniel Brandlechner

“…The article demonstrates, how mediality becomes evident through two operators: seriality and combinatorics. By placing the artist on one of the two sides of mediation, this article implicitly reverses the role long reserved for Ai Weiwei: that of the cultural mediator.…”
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Ricci Curvature on Polyhedral Surfaces via Optimal Transportation by Benoît Loisel, Pascal Romon

“…Lin, Lu and Yau and Jost and Liu have used and extended this notion for graphs, giving estimates for the curvature and, hence, the diameter, in terms of the combinatorics. In this paper, we describe a method for computing the coarse Ricci curvature and give sharper results, in the specific, but crucial case of polyhedral surfaces.…”
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Some identities on degenerate poly-Euler polynomials arising from degenerate polylogarithm functions by Lingling Luo, Yuankui Ma, Taekyun Kim, Hongze Li

“…This focus stems from their nascent importance for applications in combinatorics, number theory and in other aspects of applied mathematics. …”
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On the connectedness and diameter of a geometric Johnson graph by Crevel Bautista-Santiago, Javier Cano, Ruy Fabila-Monroy, David Flores-Peñaloza, Hernàn González-Aguilar, Dolores Lara, Eliseo Sarmiento, Jorge Urrutia

“…Combinatorics…”
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