Leonardo Cano, Rafael Diaz
Published 2016-02-29Version 1
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.
A self-dual poset on objects counted by the Catalan numbers and a type-B analogue
On some series involving the binomial coefficients $\binom{3n}{n}$
Catalan numbers and relations
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