APPLICATION OF LEXICOGRAPHIC METHODS IN FINDING NEW SOLUTIONS FOR THE CONSTRUCTION OF SWITCH FAUCETS by VLAD ANDREI CIUBOTARIU, IONEL OLARU, CRINA MARIA RADU, COSMIN GRIGORAS

“…For the elaboration and efficient use of logical-deductive methods and techniques in creativity, it is necessary to know a minimum of combinatorics, which include arrangements, combinations, permutations, graphs and finite networks. …”
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Valued Graphs and the Representation Theory of Lie Algebras by Joel Lemay

“…Quivers (directed graphs), species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. …”
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C7-Decompositions of the Tensor Product of Complete Graphs by Manikandan R.S., Paulraja P.

“…The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006) 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007) 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.…”
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The bandwidth theorem for locally dense graphs by Katherine Staden, Andrew Treglown

“…The bandwidth theorem of Böttcher, Schacht, and Taraz [Proof of the bandwidth conjecture of Bollobás and Komlós, Mathematische Annalen, 2009] gives a condition on the minimum degree of an n-vertex graph G that ensures G contains every r-chromatic graph H on n vertices of bounded degree and of bandwidth $o(n)$ , thereby proving a conjecture of Bollobás and Komlós [The Blow-up Lemma, Combinatorics, Probability, and Computing, 1999]. In this paper, we prove a version of the bandwidth theorem for locally dense graphs. …”
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Non-Abelian Topological Approach to Non-Locality of a Hypergraph State by Vesna Berec

“…To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, we have investigated the notion of non-amenability and its relation to combinatorics of dynamical self-organization for the case of fractal system of free group on finite generators. …”
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Brauer Configuration Algebras Arising from Dyck Paths by Agustín Moreno Cañadas, Gabriel Bravo Rios, Isaías David Marín Gaviria

“…The enumeration of Dyck paths is one of the most remarkable problems in Catalan combinatorics. Recently introduced categories of Dyck paths have allowed interactions between the theory of representation of algebras and cluster algebras theory. …”
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Dimension, depth and zero-divisors of the algebra of basic k-covers of a graph by Bruno Benedetti, Alexandru Constatinescu, Matteo Varbaro

“…We characterize when <em>A(G)</em> is a domain in terms of the combinatorics of <em>G</em>; it follows from a result of Hochster that when<em> A(G)</em> is a domain, it is also Cohen-Macaulay. …”
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Tensor and matrix models: a one-night stand or a lifetime romance? by Pablo Diaz

“…Exploiting recent results in combinatorics for Kronecker coefficients, we derive a formula that relates Kronecker coefficients with a hook shape with Littlewood-Richardson numbers. …”
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Pythagorean Fuzzy Matroids with Application by Muhammad Asif, Muhammad Akram, Ghous Ali

“…Additionally, we explore the concept of Pythagorean fuzzy matroids in linear algebra, graph theory, and combinatorics. Finally, we demonstrate the use of Pythagorean fuzzy matroids for minimizing the time taken by a salesman in delivering given products.…”
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APPLICATION OF LEXICOGRAPHIC METHODS IN FINDING NEW SOLUTIONS FOR THE CONSTRUCTION OF SWITCH FAUCETS by VLAD ANDREI CIUBOTARIU, IONEL OLARU, CRINA MARIA RADU, COSMIN GRIGORAS

“…For the elaboration and efficient use of logical-deductive methods and techniques in creativity, it is necessary to know a minimum of combinatorics, which include arrangements, combinations, permutations, graphs and finite networks. …”
Get full text

The Sexistential Vulnerability of Bodies in Contact in the Philosophy of Jean-Luc Nancy by Francesca Romana Recchia Luciani

“…But Nancy goes so far as to elaborate a “trans-ontology” through which the “r-existence (resistance) of sexistence” is manifested, that is to say that stubborn rejection of distinct and different bodies to the homologation and uniformity of the identical and of the identity shared by “trans-feminism” which makes its strong point of the inexhaustible combinatorics of the sexes. Thus, both for the sexistencial approach and for the transfeminist one, at the heart of every theory are the lives and practices of distinct and different sexual bodies in relation.…”
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Evaluating the number of different genomes in a metagenome by means of the compositional spectra approach. by Valery Kirzhner, Dvora Toledano-Kitai, Zeev Volkovich

“…It involves a wide range of mathematical methods, from probabilistic models of combinatorics to cluster analysis and pattern recognition techniques. …”
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Δ–Springer varieties and Hall–Littlewood polynomials by Sean T. Griffin

“…The $\Delta $ -Springer varieties are a generalization of Springer fibers introduced by Levinson, Woo and the author that have connections to the Delta Conjecture from algebraic combinatorics. We prove a positive Hall–Littlewood expansion formula for the graded Frobenius characteristic of the cohomology ring of a $\Delta $ -Springer variety. …”
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Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction by Micha Berkooz, Prithvi Narayan, Joan Simón

“…The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. …”
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Fourier series of functions involving higher-order ordered Bell polynomials by Kim Taekyun, Kim Dae San, Jang Gwan-Woo, Jang Lee Chae

“…In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). …”
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On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application by Rabha W. Ibrahim, Rafida M. Elobaid, Suzan J. Obaiys

“…Abstract Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). …”
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New Techniques for SIDH-based NIKE by Urbanik David, Jao David

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Lattice structure of Grassmann-Tamari orders by Thomas McConville

“…The Tamari order is a central object in algebraic combinatorics and many other areas. Defined as the transitive closure of an associativity law, the Tamari order possesses a surprisingly rich structure: it is a congruence-uniform lattice. …”
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The topology of Baues complexes and flip graphs by Liu, Xue (Mathematician)

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Algebraic Statistics in Practice: Applications to Networks by Casanellas, Marta, Petrović, Sonja, Uhler, Caroline

“…Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. …”
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