Relaxations of graph isomorphism by Mančinska, Laura, Šámal, Robert, Severini, Simone, Varvitsiotis, Antonios, Roberson, David E.

“…The techniques used are an interesting mix of algebra, combinatorics, and quantum information.…”
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Algorithmic problems for subsemigroups of infinite groups by Dong, R

“…</p> <p>We apply a large variety of mathematical tools in the study of these problems, ranging from Lie algebra, algebraic geometry and number theory, to combinatorics, graph theory and convex geometry. By adding these techniques into the toolbox, we are able to significantly advance the current state of art in the algorithmic theory of semigroups.…”

Analytics for characterising and measuring the naturalness of online personae by Nurse, J, Erola, A, Gibson-Robinson, T, Goldsmith, M, Creese, S

“…Specifically, we aim to conduct further assessments on the criteria through which naturalness is defined, and refine our analytics and combinatorics to measure a persona’s naturalness. We will also explore clustering approaches based on complete online personae, as a means to complement our identification of naturally occurring personae types in large datasets.…”

An efficient container lemma by Jozsef Balogh, Wojciech Samotij

“…The hypergraph container lemma, discovered independently in 2012 by David Saxton and Andrew Thomason, and by József Balogh, Robert Morris and Wojciech Samotij, is an extremely powerful tool that has been used to solve a large number of important problems in extremal combinatorics and to give simple new proofs of many others. …”
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Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics by Antonio Maria Scarfone

“…In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mrow><mo>{</mo><mi>π</mi><mo>}</mo></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the actual number of particles present in every energy level. …”
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The impact of the joint use of false aircraft targets in a group of combat unmanned aerial vehicles on the results of destruction by Volodymyr Prymirenko, Andrii Demianiuk, Roman Shevtsov, Serhii Bazilo, Petro Steshenko

“…The mathematical model uses combinatorics and binomial probability distribution. …”
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The concept «Germany» in German language textbooks for the elementary level: linguocultural markers by V. E. Shukman

“…The aim of the study is to determine which representatives form the concept Germany in German language textbooks for the elementary level, into which semantic groups they can be categorically divided and what is their quantitative ratio and combinatorics in different textbooks of this type. This aim defined such tasks as the selection of the lexical representatives of the concept Germany in all parts of the textbooks, the distribution of the selected representatives according to the categories developed during the study, the comparative analysis of the methods of verbalization (lexical filling) of the categories in relation to each textbook, and in comparison with each other and the subsequent infographic presentation of the results. …”
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When Is a Graded Free Complex Exact? by David C. Molano, Javier A. Moreno, Carlos E. Valencia

“…Unlike previous similar criteria, this one allows us to give a description of the differentials using the combinatorics of the <i>S</i>-module. The criterion is given in terms of the Betti numbers of the resolutions in each degree and the set of columns of the matrix representation of the differentials. …”
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Evolution of teaching the probability theory based on textbook by V. P. Ermakov by Tetiana Malovichko

“…The first chapter deals with combinatorics, the presentation of which does not differ much from its modern one. …”
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The inverse and derivative connecting problems for some hypergeometric polynomials by L. Bedratyuk, A. Bedratuyk

“…The connection coefficients play an important role in many problems in pure and applied mathematics, especially in combinatorics, mathematical physics and quantum chemical applications. …”
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O ENSINO DE PROBABILIDADE NOS ANOS INICIAIS: um olhar sobre a abordagem nos livros didáticos<br><I>TEACHING PROBABILITY IN EARLY SCHOOL YEARS: A LOOK AT THE APPROACH IN TEXTBOOKS<I... by Renata Moraes Santana, Rute Elizabete Souza de Rosa Borba

“…This article aims to analyze the approach to probability in Mathematics textbooks of the early years of Elementary School. 11 books of the 5th year of the National Textbook Plan Guide of 2006 were analyzed, It was observed that the ways commonly used for the introduction of probability are associated with the ideas of percentages, fractions or Combinatorics. There were also five notions that were explicitly addressed: chance, probability, random experiment, prediction and trial, with chance being the most frequent, but no collection addressed all of these notions. …”
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A general decomposition theory for the 1-2-3 Conjecture and locally irregular decompositions by Olivier Baudon, Julien Bensmail, Tom Davot, Hervé Hocquard, Jakub Przybyło, Mohammed Senhaji, Eric Sopena, Mariusz Woźniak

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Cognitive approach to developing the intelligent modules of organizational and technical systems by V. M. Trembach

“…A widely used computing paradigm contains inherent symbolic submissions of information and their processing with algorithms focused on the logic and combinatorics of procedures. This computer approach in solving some intellectual tasks is inferior to the man. …”
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Supercritical entanglement in local systems: Counterexample to the area law for quantum matter by Movassagh, Ramis, Shor, Peter Williston

“…In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. …”
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Crossing and intersecting families of geometric graphs on point sets by Álvarez-Rebollar, J. L., Cravioto-Lagos, J., Marín, N., Solé-Pi, O., Urrutia, J.

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Equivariant cohomology, homogeneous spaces and graphs by Holm, Tara Suzanne, 1975-

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Bootstrapping cascaded random matrix models: correlations in permutations of matrix products by Byrnes, Niall, Greaves, Gary Royden Watson, Foreman, Matthew R.

“…Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. …”
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Variants of Schur-Weyl duality and Dirac cohomology by Calvert, K

“…We derive the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties B_e of g. …”

Structural results for total search complexity classes with applications to game theory and optimisation by Hollender, A

“…As a direct application, we prove that NECKLACE-SPLITTING with k thieves - a notorious problem in combinatorics and fair division - lies in PPA-k under Turing reductions.…”

Assessing the Biological Value of Milk Obtained from Various Farm Animals by Orazov A., Nadtochii L., Safronova A.

“…The biological value of the milk was estimated by protein and lipid components using computational methods of food combinatorics. According to the chemical composition of the milk, camel’s milk proved to have the highest protein content (4.0%). …”
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