A continuous analogue of lattice path enumeration: Part II

Tanay Wakhare (1) , Christophe Vignat (2)

1 Department of Mathematics [College Park]
2 L2S - Laboratoire des signaux et systèmes

Following the work of Cano and Díaz, we study continuous binomial coefficients andCatalan numbers. We explore their analytic properties, including integral identities and generaliza-tions of discrete convolutions. We also conduct an in-depth analysis of a continuous analogue of thebinomial distribution, including a stochastic representation as a Goldstein-Kac process.

Domaines: Combinatoire [math.CO]

Tanay Wakhare, Christophe Vignat. A continuous analogue of lattice path enumeration: Part II. The Electronic Journal of Combinatorics, 2019. ⟨hal-02134901⟩