(k,m)-Catalan Numbers and Hook Length Polynomials for Plane Trees

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dc.creatorDu, Rosena R. X.
dc.creatorLiu, Fu
dc.date2005-01-11
dc.date2005-09-14
dc.date.accessioned2026-07-07T05:15:57Z
dc.date.available2026-07-07T05:15:57Z
dc.descriptionMotivated by a formula of A. Postnikov relating binary trees, we define the hook length polynomials for m-ary trees and plane forests, and show that these polynomials have a simple binomial expression. An integer value of this expression is C_{k,m}(n)=\frac{1}{mn+1}{(mn+1)k \choose n}, which we call the (k,m)-Catalan number. For proving the hook length formulas, we also introduce a combinatorial family, (k,m)-ary trees, which are counted by the (k,m)-Catalan numbers.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0501147
dc.identifierhttp://arxiv.org/abs/math/0501147
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73811
dc.subjectCombinatorics
dc.subject05A15, 05A19
dc.title(k,m)-Catalan Numbers and Hook Length Polynomials for Plane Trees
dc.typetext

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