More patterns in trees: Up and down, young and old, odd and even

Nachum Dershowitz*, Shmuel Zaks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We apply the tree-pattern enumeration formulæ of 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.

Original languageEnglish
Pages (from-to)447-465
Number of pages19
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2008


  • Bicolored trees
  • Binary trees
  • Bridges
  • Dyck paths
  • Lattice paths
  • Node distribution
  • Ordered trees
  • Plane-planted trees
  • Tree enumerations
  • Tree patterns


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