Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers

Details Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers

2012-04-12

arxiv.org/abs/1204.2709v1

Mathematics

Combinatorics

11 pages, 2 figures

Scientific paper

Under general conditions, the equation $g(x,y) = 0$ implicitly defines $y$ locally as a function of $x$. In this short note we study the combinatorial structure underlying a recently discovered formula for the divided differences of $y$ expressed in terms of bivariate divided differences of $g$, by analyzing the number of terms $a_n$ in this formula. The main result describes six equivalent characterizations of the sequence $\{a_n\}$.

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