More Patterns in Trees: Up and Down, Young and Old, Odd and Even | Zendy

Nachum Dershowitz | Zendy; Shmuel Zaks | Zendy

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More Patterns in Trees: Up and Down, Young and Old, Odd and Even

Author(s) -

Nachum Dershowitz,

Shmuel Zaks

Publication year - 2009

Publication title -

siam journal on discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.843

H-Index - 66

eISSN - 1095-7146

pISSN - 0895-4801

DOI - 10.1137/070687475

Subject(s) - bijection, injection and surjection , combinatorics , enumeration , mathematics , lattice (music) , tree (set theory) , extension (predicate logic) , discrete mathematics , binary tree , bijection , computer science , physics , acoustics , programming language

We apply the tree-pattern enumeration formulæof earlier work of ours [N. Dershowitz and S. Zaks, Discrete Appl. Math., 25 (1989), pp. 241-255], and a new extension thereof, to some recent enumerations of distributions of leaves in ordered trees [W. Y. C. Chen, E. Deutsch, and S. Elizalde, European J. Combin., 27 (2006), pp. 414-427] and in bicolored ordered trees [L. H. Clark, J. E. McCanna, and L. A. Székely, Bull. Inst. Combin. Appl., 21 (1997), pp. 33-45], and of distributions of up-down-up subpaths in Dyck lattice paths [Y. Sun, Discrete Math., 287 (2004), pp. 177-186]. Bijections are used to facilitate the derivation of statistics for bicolored trees.

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