Related papers: The second production matrix of a Riordan array
We construct a version of kneading theory for families of monotonous functions on the real line. The generality of the setup covers two classical results from Milnor-Thurston's kneading theory: the first one is to dynamically characterise…
We describe the period matrix and other data on a higher genus Riemann surface in terms of data coming from lower genus surfaces via an explicit sewing procedure. We consider in detail the construction of a genus two Riemann surface by…
The generalized Riordan group consists of infinite lower triangular matrices that correspond to certain operators in the space of formal power series. Each such group contains the matrix (generalized Pascal matrix), elements of which are…
The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous…
We give a relation between verbatim generating functions of what we call Pythagorean languages and matrix convexity. Namely, several multivariate matrix convex functions occurring in the existing matrix analysis literature arise naturally…
Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.
The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invariant sequences that arise are conjectured to have…
The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions…
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…
We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinatorial analysis. As a consequence, we obtain the generating…
A new product construction of graphs and digraphs, based on the standard box product of graphs and called the separated box product, is presented, and several of its properties are discussed. Questions about the symmetries of the product…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
In this paper we give a new formula for the $n$-th power of a $2\times2$ matrix. More precisely, we prove the following: Let $A= \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right )$ be an arbitrary $2\times2$ matrix, $T=a+d$ its…
First, using the method of the soliton-solution, the fermion probability density equation, which corresponds to the Dirac equation, is derived. Next, we extend the chaos theory, in which the period bifurcation is equivalent to the particle…
Frames are the most natural generalization of orthonormal bases that allow the inclusion of redundant systems. In this article, we introduce the concept of frames generated by graphs in finite-dimensional spaces and study their properties.…
The alternate row and column scaling algorithm applied to a positive $n\times n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two parameter…
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…
We discuss the folklore construction of the Gray tensor product of 2-categories as obtained by factoring the map from the funny tensor product to the cartesian product. We show that this factorisation can be obtained without using a…