Abstract
The Catalan numbers were first studied by Euler, in the context of enumerating triangulations of polygons . Among the many generalizations of this sequence, the Fuss–Catalan numbers count enumerations of dissections of polygons into -gons. In this paper, we provide a formula enumerating polygonal dissections of -gons, classified by partitions of . We connect these counts to reverse series arising from iterated polynomials. Generalizing this further, we show that the coefficients of the reverse series of polynomials enumerate colored polygonal dissections.
Citation
Alison Schuetz. Gwyn Whieldon. "Polygonal dissections and reversions of series." Involve 9 (2) 223 - 236, 2016. https://doi.org/10.2140/involve.2016.9.223
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