Related papers: Star operations on numerical semigroups: antichain…
Let $p$ be a prime number, and let $S$ be the numerical semigroup generated by the prime numbers not less than $p$. We compare the orders of magnitude of some invariants of $S$ with each other, e. g., the biggest atom $u$ of $S$ with $p$…
We present the concept of the \emph{information efficiency of functions} as a technique to understand the interaction between information and computation. Based on these results we identify a new class of objects that we call…
A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring $S$ is uniserial if and only if the matrix semiring $M_n(S)$ is uniserial. As a generalization of valuation semirings, we also…
In this paper, we consider semigroup actions of discrete countable semigroups on compact spaces by surjective local homeomorphisms. We introduce notions of continuous one-sided orbit equivalence and continuous orbit equivalence for…
Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. We explore this connection between partitions and numerical…
An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group.…
We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be…
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…
Building on work by Zagier, Bousquet-M\'elou et al., and Khamis, we give an asymptotic formula for the number of labelled interval orders on an $n$-element set.
There are many situations where comparison of different groups is of great interest. Considering the ordering of the efficiency of some treatments is an example. We present nonparametric predictive inference (NPI) for the ordering of…
Let $\mathcal{H}$ be a complex infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal H$. The star partial order is defined by $A\overset{*}{\leq}B$ if and only if…
Completing Loo-Keng Hua's approach to the real number system pioneered in 1962, this paper defines arithmetical operations directly on infinite decimals without appealing to any ordering structure. Therefore, the widespread belief that…
The immense amount of time series data produced by astronomical surveys has called for the use of machine learning algorithms to discover and classify several million celestial sources. In the case of variable stars, supervised learning…
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…
A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group $A$. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a…
One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or…
Let $S$ and $\mathcal{C}$ be affine semigroups in $\mathbb{N}^d$ such that $S\subseteq \mathcal{C}$. We provide a characterization for the set $\mathcal{C}\setminus S$ to be finite, together with a procedure and computational tools to check…
We present a natural extension of the process of taking a group quotient to arbitrary subgroups. We first review basic concepts from group theory. This will allow us to see the relationship between our new, more general quotient operation…
We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations…