Related papers: On Numerical Experiments with Symmetric Semigroups…

Recently, the concept of the $p$-numerical semigroup with $p$-symmetric properties has been introduced. When $p=0$, the classical numerical semigroup with symmetric properties is recovered. In this paper, we further study the $p$-numerical…

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $r^{th}$ Feng-Rao number is obtained.

A numerical semigroup is a submonoid of ${\mathbb Z}_{\ge 0}$ whose complement in ${\mathbb Z}_{\ge 0}$ is finite. For any set of positive integers $a,b,c$, the numerical semigroup $S(a,b,c)$ formed by the set of solutions of the inequality…

An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and a numerical semigroup is an affine semigroup with $d = 1$. A growing body of recent work examines shifted families of numerical semigroups, that is,…

Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^*$-algebra $C^*_\delta(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this…

Let \lambda be a partition of a positive integer n. Let C be a symmetric rigid tensor category over a field k of characteristic 0 or char(k)>n, and let V be an object of C. In our main result (Theorem 4.3) we introduce a finite set of…

Let 0 < a < b be two relatively prime integers and let <a,b> be the numerical semigroup generated by a and b with Frobenius number g(a,b)=ab-a-b. In this note, we prove that there exists a prime number p in <a,b> with p < g(a,b) when the…

The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…

This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…

The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$ and finding the Frobenius number is called the Frobenius problem. In this paper, we introduce the Frobenius problem for numerical…

In this article, we classify all symmetric generalized numerical semigroups in $\mathbb{N}^d$ of embedding dimension $2d+1$. Consequently, we show that in this case the property of being symmetric is equivalent to have a unique maximal gap…

Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in $\{m,m+1,\ldots, 2m-1\}.$ In this work, packed numerical semigroups are used to built the…

Let $A=(a_1, a_2, \ldots, a_n)$ be a sequence of relative prime positive integers with $a_i\geq 2$. The Frobenius number $F(A)$ is the largest integer not belonging to the numerical semigroup $\langle A\rangle$ generated by $A$. The genus…

In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups $S_n$ and of the finite Chevalley groups $GL(n,F_q)$ and…

For a nonnegative integer $p$, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_2,\dots,a_\kappa$ with $\gcd(a_1,a_2,\dots,a_\kappa)=1$ are…

There are several results in the literature concerning $p$-groups $G$ with a maximal elementary abelian normal subgroup of rank $k$ due to Thompson, Mann and others. Following an idea of Sambale we obtain bounds for the number of generators…

A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain norms or seminorms. One example is the norms on $\Z/N\Z$ introduced by Gowers in his proof of Szemer\'edi's…

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the…