Related papers: Gaps in Nonsymmetric Numerical Semigroups

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative…

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

Let $G$ be a finite abelian group, written additively, and $H$ a subgroup of~$G$. The \emph{subgroup sum graph} $\Gamma_{G,H}$ is the graph with vertex set $G$, in which two distinct vertices $x$ and $y$ are joined if $x+y\in…

Given a finitely generated (fg) group G, the set R(G) of homomorphisms from G to SL(2,C) inherits the structure of an algebraic variety known as the "representation variety" of G. This algebraic variety is an invariant of fg presentations…

We generalize the notion of symmetric semigroups, pseudo symmetric semigroups, and row factorization matrices for pseudo Frobenius elements of numerical semigroups to the case of semigroups with maximal projective dimension (MPD…

We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound…

For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an "independent" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that…

A scale-multiplicative semigroup in a totally disconnected, locally compact group $G$ is one for which the restriction of the scale function on $G$ is multiplicative. The maximal scale-multiplicative semigroups in groups acting…

It is known that a $C_0$-semigroup of Hilbert space operators is $m$-isometric if and only if its generator satisfies a certain condition, which we choose to call $m$-skew-symmetry. This paper contains two main results: We provide a…

A free numerical semigroup is a submonoid of the non-negative integers with finite complement that is additively generated by the terms in a telescopic sequence with gcd 1. However, such a sequence need not be minimal, which is to say that…

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many…

A semitopological group $G$ is called {\it an $n$-semitopological group}, if for any $g\in G$ with $e\not\in\overline{\{g\}}$ there is a neighborhood $W$ of $e$ such that $g\not\in W^{n}$, where $n\in\mathbb{N}$. The class of…

A lifting of a semilattice S is an algebra A such that the semilattice of compact (=finitely generated) congruences of A is isomorphic to S. The aim of this work is to give a categorical theory of partial algebras endowed with a partial…

In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…

Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$, with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd, then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq t(T)…

We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\'e series converges at the critical exponent $\delta_\Gamma$. We…

As well-known, in a finitary algebraic structure the set $\Gamma$ of all the non-generators is the intersection of all the maximal proper substructures. In particular, $\Gamma$ is a substructure. We show that the corresponding statements…

Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…

Let $D$ be a division ring, $n$ a positive integer, and GL$_n(D)$ the general linear group of degree $n$ over $D$. In this paper, we study the induced subgraph of the intersection graph of GL$_n(D)$ generated by all non-trivial proper…

We study the length of the gaps between consecutive members in the sumset sA when A is a pseudo s-th power sequence, with s>1. We show that, almost surely, limsup (b_{n+1}-b_{n})/log (b_n) = s^s s!/\Gamma^s(1/s), where b_n are the elements…