A Stochastic Approach to Eulerian Numbers

On the Stochastic Approach to Index Numbers

Derivatives and Eulerian Numbers

The aim of the present note is to give a closed form formula for the nth derivative of a function which satisfies Riccati’s differential equation with constant coefficients. The paper is organized as follows. In section 2 we recall the definition and basic properties of Eulerian numbers. We introduce and prove the mentioned formula in section 3. Some examples where the formula can be applied ar...

Eulerian-Catalan Numbers

We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.

Congruences on Stirling Numbers and Eulerian Numbers

In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.

Laurent polynomials and Eulerian numbers

Article history: Received 24 August 2009 Available online 25 February 2010