Related papers: Two identities of derangements

We prove astonishing identities generated by compositions of positive integers. In passing, we obtain two new identities for Stirling numbers of the first kind. In the two last sections we clarify an algebraic sense of these identities and…

We give a direct deduction and proof of two identities in the theory of plane partitions. The first one is known to enumerate the traces of plane partitions. The second one comes without any combinatorial interpretation.

This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…

We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…

We give a proof of two identities involving binomial sums at infinity conjectured by Z-W Sun. In order to prove these identities, we use a recently presented method i.e. we view the series as specializations of generating series and derive…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…

We extend our investigation of $2$-determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous…

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…

We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the…

In this paper we introduce three combinatorial models for symmetrized poly-Bernoulli numbers. Based on our models we derive generalizations of some identities for poly-Bernoulli numbers. Finally, we set open questions and directions of…

We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional…

Denote the symmetric group of degree $n$ by $S_n$. Let $\rho$ be an irreducible representation of $S_n$ over the field of complex numbers and $\sigma\in S_n$. In this paper, we describe the set of eigenvalues of $\rho(\sigma)$. Based on…

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…