Related papers: Nil-Bohr Sets of Integers
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
We continue the theory of $\tT$-systems from the work of the second author, describing both ground systems and module systems over a ground system (paralleling the theory of modules over an algebra). The theory, summarized categorically at…
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative…
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
We study properties of a sequence $\Lambda$ obtained by a randomselection of integers $n$, where $n\in\Lambda$ with probability $\varpi_{n}$, independently of the other choices. We distinguish two cases : if…
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…
This article describes a purely analytic approach to urn models of the generalized or extended P\'olya-Eggenberger type, in the case of two types of balls and constant ``balance,'' that is, constant row sum. The treatment starts from a…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…
The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
We study sets of the form $A = \big\{ n \in \mathbb N \big| \lVert p(n) \rVert_{\mathbb R / \mathbb Z} \leq \varepsilon(n) \big\}$ for various real valued polynomials $p$ and decay rates $\varepsilon$. In particular, we ask when such sets…
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in the field and residue field sort. Secondly, we deduce from a…
This article explores the connection between boolean-valued class models of set theory and the theory of arbitrary objects in roughly Kit Fine's sense of the word. In particular, it explores the hypothesis that the set theoretic universe as…