A combinatorial interpretation for a super-Catalan recurrence

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dc.creatorCallan, David
dc.date2004-08-09
dc.date.accessioned2026-07-07T05:11:09Z
dc.date.available2026-07-07T05:11:09Z
dc.descriptionNicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers (u_{n})_{n>=0}=(3,2,3,6,14,36,...): they count "aligned cubic trees" on n internal vertices. Here we give a combinatorial interpretation of the recurrence u_{n} = Sum_{k=0}^{n/2-1} ({n-2}choose{2k} 2^{n-2-2k} u_{k}): it counts these trees by number of deep interior vertices where deep interior means "neither a leaf nor adjacent to a leaf".
dc.description8 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0408117
dc.identifierhttp://arxiv.org/abs/math/0408117
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72143
dc.subjectCombinatorics
dc.subject05A15
dc.titleA combinatorial interpretation for a super-Catalan recurrence
dc.typetext

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