Related papers: Constructing the set of complete intersection nume…
In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.
Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.
We introduce the separating semigroup of a real algebraic curve of dividing type. The elements of this semigroup record the possible degrees of the covering maps obtained by restricting separating morphisms to the real part of the curve. We…
Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…
For any numerical semigroup $S$, there are infinitely many numerical symmetric semigroups $T$ such that $S=\frac{T}{2}$ is their half. We are studying the Betti numbers of the numerical semigroup ring $K[T]$ when $S$ is a 3-generated…
In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present…
Let $H$ be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization $(\RF)$ matrix for each pseudo-Frobenius element of $H.$ Further, when $H$ is symmetric and has…
We study the cyclotomic exponent sequence of a numerical semigroup $S,$ and we compute its values at the gaps of $S,$ the elements of $S$ with unique representations in terms of minimal generators, and the Betti elements $b\in S$ for which…
In this work we will introduce the concept of ratio-covariety, as a nonempty family $\mathscr{R}$ of numerical semigroups verifying certain properties. This concept will allow us to: \begin{enumerate} \item Describe an algorithmic process…
We construct immersions of trivalent abstract tropical curves in the Euclidean plane and embeddings of all abstract tropical curves in higher dimensional Euclidean space. Since not all curves have an embedding in the plane, we define the…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…
We consider numerical semigroups $S_3 = \langle d_1,d_2,d_3\rangle$, minimally generated by three positive integers. We revisit the Wilf question in $S_3$ and, making use of identities for degrees of syzygies of such semigroups, give a…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
This work generalizes the short resolution given in Proc. Amer. Math. Soc. \textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a characterization of Ap\'{e}ry sets is given. This characterization lets compute Ap\'{e}ry…
That announcement gives the structure of totally reducible linear Lie algebras which are the Lie algebra of the holonomy group of (at least) one torsion-free connection. The result uses the (already known) classi cation of the irreducible…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…
In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the…
In this paper, we carry out a fairly comprehensive study of two special classes of numerical semigroups, one generated by the sequence of partial sums of an arithmetic progression and the other one generated by the partial sums of a…