English

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.

Keywords

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}
}
R2 v1 2026-06-22T13:00:16.993Z