Related papers: Numerical Semigroups with unique Ap\'{e}ry expansi…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroup of [7]. Several…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
Attached to a singular analytic curve germ in $d$-space is a numerical semigroup: a subset $S$ of the non-negative integers which is closed under addition and whose complement isfinite. Conversely, associated to any numerical semigroup $S$…
Let $G$ be a multiplicative subgroup of the prime field $\mathbb F_p$ of size $|G|> p^{1-\kappa}$ and $r$ an arbitrarily fixed positive integer. Assuming $\kappa=\kappa(r)>0$ and $p$ large enough, it is shown that any proportional subset…
Let $P$ be a finite $p$-group and $p$ be an odd prime. Let $\mathcal{A}_p(P)_{\geq2}$ be a poset consisting of elementary abelian subgroups of rank at least 2. If the derived subgroup $P'\cong C_p\times C_p$, then the spheres occurring in…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
A numerical semigroup is said to be ordinary if it has all its gaps in a row. Indeed, it contains zero and all integers from a given positive one. One can define a simple operation on a non-ordinary semigroup, which we call here the…
In this article, we study the quotients of numerical semigroups, generated by two coprime positive numbers, named (a,b) over d. We give formulae for the usual invariants of these semigroups, expressed in terms of continued fraction…
We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension of every numerical semigroup with Frobenius number at most…
We introduce a symmetry class for higher dimensional partitions - fully complementary higher dimensional partitions (FCPs) - and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define…
Fixed two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. Besides, the semigroups where…
The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions…
Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is said to be an additive complement of the set $A$ if all sufficiently large natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in B$. This…
In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the root…
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complement is called its Frobenius number. We consider the set of…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
In this paper, we generalize the work of Tuenter to give an identity which completely characterizes the complement of a numerical semigroup in terms of its Ap\'ery sets. Using this result, we compute the $m$th power Sylvester and…