Related papers: Computing congruences of finite inverse semigroups
In this paper, we describe an algorithm for computing the left, right, or 2-sided congruences of a finitely presented semigroup or monoid with finitely many classes, and an alternative algorithm when the finitely presented semigroup or…
We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…
We give an efficient algorithm for the enumeration up to isomorphism of the inverse semigroups of order n, and we count the number S(n) of inverse semigroups of order n<=15. This improves considerably on the previous highest-known value…
In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…
We give several algorithms addressing computations of intersections of conjugate subgroups.
In this paper we provide an account of the Todd-Coxeter algorithm for computing congruences on semigroups and monoids. We also give a novel description of an analogue for semigroups of the so-called Felsch strategy from the Todd-Coxeter…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and…
We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP
For a given inverse semigroup, one can associate an \'etale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated \'etale groupoids. In this paper, we focus on…
By suitable examples we illustrate an algorithm for composition of inverse problems.
For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of, seed, by broadening the notion of generator. This new concept allows us to explore the semigroup tree in an alternative…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.