Related papers: A Note on Generating Sets for Semiflows
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…
The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…
It is shown that a finitely generated branch group has Serre's property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group…
We provide a structure theorem for all almost complete intersection ideals of depth three in any Noetherian local ring. In particular, we find that the minimal generators are the pfaffians of suitable submatrices of an alternating matrix.…
The algebraic extension $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}}$ of the extended bicyclic semigroup for an arbitrary $\omega$-closed family $\mathscr{F}$ subsets of $\omega$ is introduced. It is proven that…
In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more…
We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical…
In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We…
We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to…
We study the monotone skew-product semiflow generated by a family of neutral functional differential equations with infinite delay and stable D-operator. The stability properties of D allow us to introduce a new order and to take the…
The theory of free-choice Petri nets is an established field, initiated in the 1970s by Commoner and Hack at MIT. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new…
To a finitely generated profinite group $G$, a formal Dirichlet series $P_G(s)=\sum_{n \in \mathbb N} {a_n(G)}/{n^s}$ is associated, where $a_n(G)=\sum_{|G:H|=n}\mu(H, G)$ and $\mu(H,G)$ denotes the M\"obius function of the lattice of open…
We present $c_0$--semigroup generation results for the free streaming operator with abstract boundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with a lot of examples and…
Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of…
Some new results on metric ultraproducts of finite simple groups are presented. Suppose that G is such a group, defined in terms of a non-principal ultrafilter {\omega} on N and a sequence {(G_i)_{i \in N}} of finite simple groups, and that…
Various equivalent conditions for a semigroup or a resolvent generated by a Markov process to be of Feller type are given.
We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map $(T,M,\mu)$, where $\mu$ is a Gibbs measure, an aperiodic H\"older continuous cocycle…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
A countable group $G$ is said to be \emph{matricial field} (MF) if it admits a strongly converging sequence of approximate homomorphisms into matrices; i.e, the norms of polynomials converge to those in the left regular representation. $G$…
An $f$-subgroup is a linear recurring sequence subgroup, a multiplicative subgroup of a field whose elements can be generated (without repetition) by a linear recurrence relation, with characteristic polynomial $f$. It is called…