Related papers: Numerical Semigroups with unique Apery expansions …
We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…
Entringer numbers occur in the Andr\'e permutation combinatorial set-up under several forms. This leads to the construction of a matrix-analog refinement of the tangent (resp. secant) numbers. Furthermore, closed expressions for the…
We introduce a new class of semigroups arising from a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups." We show that the class of synchronous automaton semigroups is strictly contained in…
This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius…
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…
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…
In this paper we introduce a particular semigroup transform $\mathcal{A}$ that fixes the invariants involved in Wilf's conjecture, except the embedding dimension. It also allows one to arrange the set of not ordinary and not irreducible…
In this paper, we introduce and study new classes of Ap\'ery-type series involving the multiple $t$-harmonic sums by combining the methods of iterated integral and Fourier--Legendre series expansions, where the multiple $t$-harmonic sums…
Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial…
We provide a new way to represent numerical semigroups by showing that the position of every Ap\'ery set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this…
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…
Given a numerical semigroup ring $R=k[\![S]\!]$, an ideal $E$ of $S$ and an odd element $b \in S$, the numerical duplication $S \! \Join^b \! E$ is a numerical semigroup, whose associated ring $k[\![S \! \Join^b \! E]\!]$ shares many…
Given a one-dimensional Cohen-Macaulay local ring we compare several sets of invariants (micro-invariants, Apery invariants and invariants of the tangent cone) and give explicit formulas relating them. We show that, in fact, they coincide…
We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a common finite bound for the rank of…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
A finite transitive permutation group is elusive if it contains no derangements of prime order. These groups are closely related to a longstanding open problem in algebraic graph theory known as the Polycirculant Conjecture, which asserts…
Consider a numerical semigroup minimally generated by a subset of the interval $[e,2e-1]$ with multiplicity $e$ and width $e-1$. Such numerical semigroups are called Sally type semigroups. We show that the defining ideals of these semigroup…
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
We investigate additive properties of sets $A,$ where $A=\{a_1,a_2,\ldots ,a_k\}$ is a monotone increasing set of real numbers, and the differences of consecutive elements are all distinct. It is known that $|A+B|\geq c|A||B|^{1/2}$ for any…