Related papers: Algorithmic Problems in Amalgams of Finite Groups
In this paper we provide an algorithm to classify groups of points on abelian threefolds over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $\mathbb{F}_q$-isogeny class. This work…
A new bound for the rank of the intersection of finitely generated subgroups of a free group is given, formulated in topological terms, and very much in the spirit of Stallings. The bound is a contribution to (although unfortunately not a…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings'…
Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…
We generalize Philip Hall's celebrated theorems on finite solvable groups to scheme theory. Our result is based on a series of results on hypergroups.
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for…
The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…
For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic,…
RecentadvancesinDistributedComputinghighlightmodelsandalgo- rithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms…
Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited to studying local properties of general finite groups. We…
This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Grigorchuk.
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
Predicting the cheapest sample size for the optimal stratification in multivariate survey design is a problem in cases where the population frame is large. A solution exists that iteratively searches for the minimum sample size necessary to…