Continuous Analogues for the Binomial Coefficients and the Catalan Numbers
Combinatorics
2016-04-26 v4 Mathematical Physics
Differential Geometry
math.MP
Probability
Abstract
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an application we develop a continuous analogue for the binomial distribution.
Cite
@article{arxiv.1602.09132,
title = {Continuous Analogues for the Binomial Coefficients and the Catalan Numbers},
author = {Leonardo Cano and Rafael Diaz},
journal= {arXiv preprint arXiv:1602.09132},
year = {2016}
}