Related papers: Applications of computational tools for finitely p…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…
In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely…
Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients.
In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally strongly noetherian adic space.
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes of a tutorial I gave at the NATO Advanced Study Institute on…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…
A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…
Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understanding of free resolutions by providing, for example,…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
We describe a new approach towards the systematic construction of finite groups up to isomorphism. This approach yields a practical algorithm for the construction of finite solvable groups up to isomorphism. We report on a GAP…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…
We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…
Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…
The absolute Galois group Gal$(\overline{\mathbb{Q}}/\mathbb{Q})$ of the field $\mathbb{Q}$ of rational numbers can be presented as a highly computable object, under the notion of type-2 Turing computation. We formalize such a presentation…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…