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(k,m)-Catalan Numbers and Hook Length Polynomials for Plane Trees | | Rosena R.X. Du
; Fu Liu
; | | Date: |
11 Dec 2004 | | Subject: | Combinatorics MSC-class: 05A15, 05A19 | math.CO | | Abstract: | Motivated 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. | | Source: | arXiv, math.CO/0501147 | | Services: | Forum | Review | PDF | Favorites | |
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