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Symmetric linear operator identities in quasigroups

Reza Akhtar (2017)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a quasigroup. Associativity of the operation on $G$ can be expressed by the symbolic identity $R_{x} L_{y} = L_{y} R_{x}$ of left and right multiplication maps; likewise, commutativity can be expressed by the identity $L_{x} = R_{x}$ . In this article, we investigate symmetric linear identities: these are identities in left and right multiplication symbols in which every indeterminate appears exactly once on each side, and whose sides are mirror images of each other. We determine precisely which identities imply associativity and...

Symmetric monoidal completions and the exponential principle among labeled combinatorial structures.

Menni, Matías (2003)

Theory and Applications of Categories [electronic only]

Symmetric partitions and pairings

Ferenc Oravecz (2000)

Colloquium Mathematicae

The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

Symmetric polynomials and divided differences in formulas of intersection theory

Piotr Pragacz (1996)

Banach Center Publications

The goal of this paper is at least two-fold. First we attempt to give a survey of some recent (and developed up to the time of the Banach Center workshop Parameter Spaces, February '94) applications of the theory of symmetric polynomials and divided differences to intersection theory. Secondly, taking this opportunity, we complement the story by either presenting some new proofs of older results (and this takes place usually in the Appendices to the present paper) or providing some new results which...

Symmetric powers of cyclic sets and product decompositions of generating functions. (Symmetrische Potenzen zyklischer Mengen und Produktzerlegungen von erzeugenden Funktionen.)

Siebeneicher, Christian (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

Symmetric subsets of lattice paths.

Verbitsky, Oleg (2000)

Integers

Symmetric sum-free partitions and lower bounds for Schur numbers.

Fredricksen, Harold, Sweet, Melvin M. (2000)

The Electronic Journal of Combinatorics [electronic only]

Symmetric translation nets.

Dieter Jungnickel (1982)

Journal für die reine und angewandte Mathematik

Symmetries in Steinhaus triangles and in generalized Pascal triangles.

Brunat, Josep M., Maureso, Montserrat (2011)

Integers

Symmetries of embedded complete bipartite graphs

Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn (2014)

Fundamenta Mathematicae

We characterize which automorphisms of an arbitrary complete bipartite graph $K_{n, m}$ can be induced by a homeomorphism of some embedding of the graph in S³.

Symmetries of random discrete copulas

Arturo Erdely, José M. González–Barrios, Roger B. Nelsen (2008)

Kybernetika

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

Symmetries of woven fabrics

Bohdan Zelinka (1984)

Aplikace matematiky

Symmetrische Zerlegung von Kettenprodukten.

Martin Aigner (1975)

Monatshefte für Mathematik

Symmetrized and continuous generalization of transversals

Martin Kochol (1996)

Mathematica Bohemica

The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.

Symmetry and unimodality in the $q, x, y$ -hit numbers.

Butler, Fred (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Symmetry breaking in graphs.

Albertson, Michael O., Collins, Karen L. (1996)

The Electronic Journal of Combinatorics [electronic only]

Symmetry of iteration graphs

Walter Carlip, Martina Mincheva (2008)

Czechoslovak Mathematical Journal

We examine iteration graphs of the squaring function on the rings $ℤ / n ℤ$ when $n = 2^{k} p$ , for $p$ a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when $k = 3$ and when $k \geq 5$ and are symmetric when $k = 4$ .

Systèmes aux $q$ -différences singuliers réguliers : classification, matrice de connexion et monodromie

Jacques Sauloy (2000)

Annales de l'institut Fourier

G.D. Birkhoff a posé, par analogie avec le cas classique des équations différentielles, le problème de Riemann-Hilbert pour les systèmes “fuchsiens” aux $q$ -différences linéaires, à coefficients rationnels. Il l’a résolu dans le cas générique: l’objet classifiant qu’il introduit est constitué de la matrice de connexion $P$ et des exposants en $0$ et $\infty$ . Nous reprenons sa méthode dans le cas général, mais en traitant symétriquement $0$ et $\infty$ et sans recours à des solutions à croissance “sauvage”. Lorsque $q$ ...

Szemerédi theorem implies Furnsternberg theorem

Volný, Dalibor (1981)

Abstracta. 9th Winter School on Abstract Analysis

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