Related papers: Courte preuve d'une identit\'{e} comportant les no…

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…

Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…

An identity for binomial symbols modulo an odd positive integer $n$ relating to the least prime factor of $n$ is proved. The identity is discussed within the context of Pell conics.

We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…

In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers $(a,b,c)$ with $a+b+c=n-1$, $n\ge 4$. These identities are deduced while translating into homotopical terms the gauge action on the…

We present an identity which can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity. We give a proof using the complex analysis.

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.

In this paper we study properties of numbers $K_n^l$ of connected components of bifurcation diagrams for multiboundary singularities $B_n^l$. These numbers generalize classic Bernoulli-Euler numbers. We prove a recurrent relation on the…

We obtain simple proofs of certain inequalites for bivariate means.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.

We prove a new universal identity for umbral operators. This motivates the definition of a subclass satisfying a simplified identity, which we fully characterize. The results are illustrated with common examples of the theory of umbral…

We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…

Making use of the theory of infinitesimal canonical transformations, a concise proof is given of Jacobi's identity for Poisson brackets.

We present a simple proof and a generalization of a Menon-type identity by Li, Hu and Kim, involving Dirichlet characters and additive characters.

Given an odd prime p, we present three independent ways of relating modulo p certain truncated convolutions of divided Bernoulli numbers to certain full convolutions of divided Bernoulli numbers.

We give alternative proof of Melham's and Howard's identities on generalised Fibonacci numbers

We produce a new, shorter construction of a minor-universal planar graph.