Brown's Theorem and its Application for Enumeration of Dissections and Planar Trees

Evgeniy Krasko, Alexander Omelchenko

Abstract


We present new functional equations connecting the counting series of plane and planar (in the sense of Harary and Palmer) dissections. Simple rigorous expressions for counting symmetric $r$-dissections of polygons and planar $S$-dissections are obtained.

Keywords


planar dissections; plane trees; enumeration

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