Related papers: Generalized Riordan arrays and zero generalized Pa…
We introduce a family of generalized Broughton polynomials and compute the characteristic varieties of complement of a curve arrangement defined by fibers of some generalized Broughton polynomials
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
Jean-Louis Loday has defined generalised bialgebras and proved structure theorems in this setting which can be seen as general forms of the Poincar\'e-Birkhoff-Witt and the Cartier-Milnor-Moore theorems. It was observed by the present…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
In this paper, we present k sequences of Generalized Van der Laan Polynomials and Generalized Perrin Polynomials using Genaralized Fibonacci and Lucas Polynomials. We give some properties of these polynomials. We also obtain generalized…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers $r,n\geq 0$, we conjecture that $L_n^{(-1-n-r)}(x) = \sum_{j=0}^n \binom{n-j+r}{n-j}x^j/j!$ is a…
We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of…
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons.…
A matrix polynomial is a polynomial in a complex variable $\lambda$ with coefficients in $n \times n$ complex matrices. The spectral curve of a matrix polynomial $P(\lambda)$ is the curve $\{ (\lambda, \mu) \in \mathbb{C}^2 \mid…
Riordan matrices are infinite lower triangular matrices that correspond to certain operators in the space of formal power series. In this paper, we introduce similar matrices for the space of formal Dirichlet series. We show that these…
Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
The general properties of the ordinary and generalized parafermionic algebras are discussed. The generalized parafermionic algebras are proved to be polynomial algebras. The ordinary parafermionic algebras are shown to be connected to the…
Let $\tau$ be a strongly $(n,p;a,c)$ regular graph,such that $0<c<p<n-1,$ $A$ his matrix of adjacency and let ${\cal V}_{n}$ be the Euclidean space spanned by the powers of $A$ over the reals where the scallar product $\bullet|\bullet$ is…
We define a general notion of centrally $\Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $\Gamma$…
We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan numbers. We investigate the Hankel transforms of many of the recurrence solutions, and…
We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of…
A Riordan array is defined by its production matrix. In this paper, we explore the notion of the second production matrix of a Riordan array, characterizing the matrix that is generated by it. We indicate how this procedure can be…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…