Related papers: A method for building permutation representations …

Consider a discrete valuation ring $R$ whose residue field is finite of cardinality at least $3$. For a finite torsion module, we consider transitive subsets $O$ under the action of the automorphism group of the module. We prove that the…

In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $1\frac{1}{2}$-designs). Using this new method, we construct several infinite families of partial geometric…

We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…

We give a characterization of a matroid to be paving, through its set of hyperplanes and give an algorithm to construct all of them.

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ the…

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are…

In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations…

In this article we define $G$-algebras, that is, graded algebras on which a reductive group $G$ acts as gradation preserving automorphisms. Starting from a finite dimensional $G$-module $V$ and the polynomial ring $\mathbb{C}[V]$, it is…

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

This paper extends previous work with network fragments and situation-specific network construction. We formally define the asymmetry network, an alternative representation for a conditional probability table. We also present an…

Let $G$ be a finite reductive group defined over $\mathbb{F}_q$, with $q$ a power of a prime $p$. Motivated by a problem recently posed by C. Curtis, we first develop an algorithm to express each element of $G$ into a canonical form in…

For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of abelian o-groups equipped with further structure. This generalizes the corresponding result of…

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

We describe an algorithm that, given a k-tuple of permutations representing the monodromy of a rational map, constructs an arbitrarily precise floating-point complex approximation of that map. We then explain how it has been used to study a…

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not. Given a finitely generated subgroup G of a finite product of limit groups, we…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph. A key ingredient is a new motion planning algorithm whose…

We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of their proofs, we obtain some combinatorial results.