Related papers: Dominic Welsh: his work and influence

We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by B\"{o}gel, already from the 1930s, on an alternative higher dimensional calculus of real functions, a…

We introduce a class of continuous planar processes, called "semimartingales on rays", and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such planar processes are…

This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek…

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

In this expository paper, we provide the readers with an overview of Dennis Sullivan's major contributions to the area of Dynamical Systems.

We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a new combinatorial characterization of the class of split…

In the last years it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as Physics, Population Dynamics, Chemistry…

We review the properties of six families of orthogonal polynomials that form the main bulk of the collection called the Askey--Wilson scheme of polynomials. We give connection coefficients between them as well as the so-called linearization…

A collection of brilliant and original unfinished ideas by Wladyslaw Marcinek (1952-2003) in particle interactions, categorical approach to generalized statistics, qubits and quantum logic, entwined operators, cobordisms and noncommutative…

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death,…

In the 1970s, William Tutte developed a clever algebraic approach, based on certain "invariants", to solve a functional equation that arises in the enumeration of properly colored triangulations. The enumeration of plane lattice walks…

The present paper aims at establishing formal connections between correspondence phenomena, well known from the area of modal logic, and the theory of display calculi, originated by Belnap. These connections have been seminally observed and…

Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star…

It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a…

The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is…

These are notes and slides from a Pecha-Kucha talk given on March 6, 2013. The presentation tinkered with the question whether calculus on graphs could have emerged by the time of Archimedes, if the concept of a function would have been…

We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald $P$-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our…

This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…

Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the orthonormalization constants for these…

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…