Related papers: Double groupoids, matched pairs and then matched t…

A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…

In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…

Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…

I characterize the combinatorially complete pargoids (partial applicative systems) by expandability with two constants that satisfy the well-known identities. An example shows that this class contains more than just the reducts of partial…

A travel groupoid is an algebraic system satisfying two suitable conditions, which has a relation to graphs. In this article, we characterize travel groupoids on finite complete multipartite graphs, and we give the numbers of travel…

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. This extends previous work that appeared in math.QA/0308228. Several important classes of examples of tensor…

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the…

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.

We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple,…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

In this paper the category of opposite brace triples is introduced in a general braided monoidal setting. Under cocommutativity, it is proved to be isomorphic to the category of Hopf braces. Furthermore, if one considers the subcategories…

Kuz'min (1996) characterized groups having Wirtinger presentations in relation to their second group homology. In this paper, we further refine the relation between these groups and their second group homology.

We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…

Double pants decompositions were introduced in our paper "Double pants decompositions of 2-surfaces" (Mosc. Math. J. 11 (2011), no. 2, 231-258, arXiv:1005.0073), together with a flip-twist groupoid acting on these decompositions. It was…

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.