Related papers: The arithmetic extensions of a numerical semigroup
In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of…
We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…
Let $a$ be a positive element in a unital $C^*$-algebra $\mathfrak{A}$. We define a semi-norm on $\mathfrak{A}$, which generalizes the $a$-operator semi-norm and the $a$-numerical radius. We investigate basic properties of this semi-norm…
We derive the lower bound for Frobenius number of symmetric (not complete intersection) semigroups generated by four elements.
This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.
We compute the Frobenius number for numerical semigroups generated by the squares of three consecutive Fibonacci numbers. We achieve this by using and comparing three distinct algorithmic approaches: those developed by Ram\'irez Alfons\'in…
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the…
We classify the semifields and division semirings containing the max-plus semifield $\mathbb{Z}_\mathrm{max}$, which are finitely generated as $\mathbb{Z}_\mathrm{max}$-semimodules.
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…
For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of semigroup elements. This work generalizes many…
Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.
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,…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
If $m \in \mathbb{N}$ and $A$ is a finite subset of $\bigcup_{k \in \mathbb{N} \setminus \{0,1\}} \{1,\ldots,m-1\}^k$, then we denote by \begin{align*} \mathscr{C}(m,A) = \left\{S\in \mathscr{S}_m \mid s_1+\cdots+s_k-m \in S \mbox{ if }…
I present an algorithm based on sector decomposition and Mellin-Barnes techniques to power expand Feynman integrals. The coefficients of this expansion are given in terms of finite integrals that can be calculated numerically. I show in an…
This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three…
The notion of formal Siegel modular forms for an arithmetic subgroup $\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the…
The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including…
In this paper we present a new algorithm to calculate the set of Arf numerical semigroups with given conductor. Moreover, we extend the previous problem to the class of good semigroups, presenting procedures to compute the set of the Arf…
We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…