Related papers: Heun functions and combinatorial identities
In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe…
Combinatorial categories satisfy a stronger form of Yoneda Lemma, namely, the isomorphism type of an object can be recovered by counting the number of homomorphisms from all other objects into it. In this work, we show that this property…
Identities involving Mobius function values (u(j),u(k)) are used to generate a Riemann Hypothesis equivalent.
We study two techniques to obtain new families of classical and general Dual-Feasible Functions: A conversion from minimal Gomory--Johnson functions; and computer-based search using polyhedral computation and an automatic maximality and…
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.
In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \begin{equation*}…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
Recently N.Jing discovered a certain combinatorial identity from validity of the Serre relations in some vertex representations of quantum Kac-Moody algebras. We generalize this identity, in particular, extending it from polynomials to…
We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It…
We present a summation rule using the Mellin transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the…
We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities,…
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
For a covariant functor W. Fulton and R. MacPherson defined \emph{an operational bivariant theory} associated to this covariant functor. In this paper we will show that given a contravariant functor one can similarly construct a ``dual"…