Related papers: Bivariate $P$-polynomial association schemes
We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
A graph $X$ is said to be a pattern polynomial graph if its adjacency algebra is a coherent algebra. In this study we will find a necessary and sufficient condition for a graph to be a pattern polynomial graph. Some of the properties of the…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…
We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…
We introduce a two-parameters bt-algebra which, by specialization, becomes the one-parameter bt-algebra, introduced by the authors, as well as another one-parameter presentation of it; the invariant for links and tied links, associated to…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
An analytic classification of generic anti-polynomial vector fields $\dot z = \overline{P(z)}$ is given in term of a topological and an analytic invariants. The number of generic strata in the parameter space is counted for each degree of…
In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…
In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric…
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
There are three families of bivariate polynomial maps associated with the rank-$2$ simple complex Lie algebras $A_2, B_2 \cong C_2$ and $G_2$. It is known that the bivariate polynomial map associated with $A_2$ induces a permutation of…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
Coherent configurations are a generalization of association schemes. In this paper, we introduce the concept of $Q$-polynomial coherent configurations and study the relationship among intersection numbers, Krein numbers, and eigenmatrices.…
It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we…
In this paper, the study of bivariate generalised beta type I and II distributions is extended to the complex matrix variate case, for which the corresponding density functions are found. In addition, for complex bimatrix variate beta type…
In this short paper, we establish connection formulae for trivariate $q$-polynomials.
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…