Continuous Analogues for the Binomial Coefficients and the Catalan Numbers

2016/02/29 by Leonardo Cano, Cano, Leonardo, Rafael Díaz +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.1602.09132

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.

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