Related papers: Touchard like polynomials and generalized Stirling…
Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…
A general solution is found for a large class of time continuous autonomous nonlinear dynamical systems, the so-called quasi-polynomial systems. This solution is expressed in terms of a new type of special functions defined via their Taylor…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
In Combinatorics Stirling numbers may be defined in several ways. One such definition is given in [1], where an extensive consideration of Stirling numbers is presented. In this paper an alternative definition of Stirling numbers of both…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of…
We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and…
We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring invariant in that case. The polynomial is an invariant of a…
The Stirling numbers of type $B$ of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as well as Broder's $r$-version of these numbers. Among these…
Exploiting the fact that the $q$-Whittaker polynomials arise as a specialization of the (modified) Macdonald polynomials, we derive some of their basic properties, and explore interesting identities that they satisfy. We also show how they…
We give a direct and simple proof of Touchard's continued fraction, provide an extension of it, and transform it into similar expansions related to Motzkin and Schroeder numbers. Another proof is then given that uses only induction. We use…
Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and…
We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus $\mathbb{T}^d$, as well as that of their square roots. These estimates arise from the spectral analysis of the quasi-periodic Schr\"odinger and the…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
We introduce a generalization $\pounds_{d}^{(\alpha)}(X)$ of the finite polylogarithms $\pounds_{d}^{(0)}(X)=\pounds_d(X)=\sum_{k=1}^{p-1}X^k/k^d$, in characteristic $p$, which depends on a parameter $\alpha$. The special case…
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…
The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed category E, is generalised for E just having pullbacks. The 2-categorical analogue of the theory of polynomials and polynomial functors is given, and…
In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, $r$-Whitney numbers,…
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
We introduce a 'grading switching' for arbitrary nonassociative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. We take inspiration from a fundamental tool in the classification theory of…