Continuous Analogues for the Binomial Coefficients and the Catalan Numbers

Applicable Analysis and Discrete Mathematics

article

Rafael Diaz¹  Leonardo Cano² 

[1] Universidad Nacional de Colombia – Sede Medell´ın;Universidad Nacional de Colombia – Sede Bogot´a, Facultad de Ciencias, Departamento de Matem´aticas

关键词: Gaussian Distribution;    Convex Polytopes;    lattice paths;    Catalan numbers;    Binomial coefficients;   

DOI  :  10.2298/AADM161015019D

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Using techniques from the theories of convex polytopes, lattice paths, andindirect influences on directed manifolds, we construct continuous analoguesfor the binomial coefficients and the Catalan numbers. Our approach forconstructing these analogues can be applied to a wide variety of combinatorial sequences. As an application we develop a continuous analogue for thebinomial distribution.

【 授权许可】

Unknown