Some identities for the Catalan and Fine numbers

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dc.creatorCallan, David
dc.date2005-02-25
dc.date.accessioned2026-07-07T05:17:28Z
dc.date.available2026-07-07T05:17:28Z
dc.descriptionWe establish combinatorial interpretations of several identities for the Catalan and Fine numbers and, along the way, we present some new bijections of independent interest. Briefly, we show that C_{n} = 1/(n+1) Sum_{k} (n+1)choose(2k+1) (n+k)choose(k) counts ordered trees on n edges by number of interior vertices adjacent to a leaf, and C_{n} = 2/(n+1) Sum_{k} (n+1)choose(k+2) (n-2)choose(k) counts Dyck n-paths by number of long interior inclines. We also give an analogue for the Fine numbers of Touchard's Catalan number identity.
dc.descriptionLaTeX, 17 pages
dc.identifierhttps://arxiv.org/abs/math/0502532
dc.identifierhttp://arxiv.org/abs/math/0502532
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74319
dc.subjectCombinatorics
dc.subject05A19;05A15
dc.titleSome identities for the Catalan and Fine numbers
dc.typetext

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