Related papers: Gapset Extensions, Theory and Computations
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…
In this work we introduce the notion of almost-symmetry for generalized numerical semigroups. In addition to the main properties occurring in this new class, we present several characterizations for its elements. In particular we show that…
We study statistical properties of numerical semigroups of genus $g$ as $g$ goes to infinity. More specifically, we answer a question of Eliahou by showing that as $g$ goes to infinity, the proportion of numerical semigroups of genus $g$…
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 a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
Based on the gauge semi-simple tensor extension of the Poincar\'e group another alternative approach to the cosmological term problem is proposed.
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
Convex algebras, also called (semi)convex sets, are at the heart of modelling probabilistic systems including probabilistic automata. Abstractly, they are the Eilenberg-Moore algebras of the finitely supported distribution monad.…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of…
In this paper, we extend recent results about the distribution of even and odd gaps of a numerical semigroup. We find that, for any numerical semigroup, the distribution can be computed in terms of the numbers of or the sums of odd and even…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
There has been significant recent interest in studying how the number of numerical semigroups of genus $g$ behaves as a function of $g$. Bras-Amor\'os has shown how to organize the collection of numerical semigroups of genus $g$ into a…
The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such…
The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…
In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing…
The main results in this thesis deal with the representation growth of certain classes of groups. In chapter $1$ we present the required preliminary theory. In chapter $2$ we introduce the Congruence Subgroup Problem for an algebraic group…
In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present…
A numerical semigroup is a submonoid of $\mathbb N$ with finite complement in $\mathbb N$. A generalized numerical semigroup is a submonoid of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. In the context of numerical…