Related papers: The Multiple Riordan Group and the Multiple Riorda…
Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group…
We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result presented in A332636, ii) provides a complete set of…
In this article, we provide characterizations of toric Richardson varieties across all types through three distinct approaches: 1) poset theory, 2) root theory, and 3) geometry.
In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.
We redefine a multiplicative group structure on the set of equivalence classes of rational sequences satisfying a fixed linear recurrence of degree two, which was defined by R. R. Laxton in his paper "On groups of linear recurrences I"…
We show how to define, for every Riordan group element $(g(x), f(x))$, an involution in the Riordan group. More generally, we show that for every pseudo-involution $P$ in the Riordan group, we can define a new involution beginning with an…
In this paper, we study symmetric lattice paths. Let $d_{n}$, $m_{n}$, and $s_{n}$ denote the number of symmetric Dyck paths, symmetric Motzkin paths, and symmetric Schr\"oder paths of length $2n$, respectively. By using Riordan group…
The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.
In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
This paper is a continuation of the paper "Numerical Semigroups: Ap\'ery Sets and Hilbert Series". We consider the general numerical AA-semigroup, i.e., semigroups consisting of all non-negative integer linear combinations of relatively…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
We give an overview of a number of Schreier-type extensions of monoids and discuss the relation between them. We begin by discussing the characterisations of split extensions of groups, extensions of groups with abelian kernel and finally…
When $p(t)$ is a polynomial of degree $d$, $k$-th column of the Riordan array $\bigl(1/(1 - t^{d+1}), tp(t)\bigr)$ is an eventually periodic sequence with the repeating part beginning at the $1 + (k-1)(d+1)$-st term. The pre-periodic terms…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we…
This paper studies two families of constraints for two-dimensional and multidimensional arrays. The first family requires that a multidimensional array will not contain a cube of zeros of some fixed size and the second constraint imposes…
Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…
We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…