Related papers: On some combinatorial properties of the orbits on …
Let $(V,\gamma )$ be a real finite dimensional vector space with a symmetric bilinear form $\gamma $ whose kernel is spanned by a nonzero vector. The set of invertible real linear mappings of $(V, \gamma )$ into itself forms a Lie group…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
Ramsey algebras is an attempt to investigate Ramsey spaces generated by algebras in a purely combinatorial fashion. Previous studies have focused on the basic properties of Ramsey algebras and the study of a few specific examples. In this…
Our goal is to find a representative of each orbit of the coadjoint action of the generalized Galile group on the dual of its Lie algebra. Our line of argument follows that of Cushman and van der Kallen, but differs in the details.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup $\Omega$ (generalization of matching or family associative algebras) or in its cartesian square…