Related papers: Farey Recursive Functions
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in the length of the chain. These relations…
A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We show that certain Riordan arrays have generating functions that can be expressed as continued fractions of Jacobi and Thron type. We investigate the inverses of such arrays, which in certain circumstances can also have generating…
Rational approximations of generalized hypergeometric functions ${}_pF_q$ of type $(n+k,k)$ are constructed by the Drummond and factorial Levin-type sequence transformations. We derive recurrence relations for these rational approximations…
The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
In this study, several interesting iterative sequences were investigated. First, we define the iterative sequences. We fix function f(n). An iterative sequence starts with a natural number n, and calculates the sequence f(n),f(f(n)),…
The recursion relations are derived for multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level.…
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…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their…
We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper,…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
We present explicit formulas for the computation of the neighbors of several elements of Farey subsequences.
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…