Pleine trees and reduction rules

Nelson Y. Li, Toufik Mansour, Augustine O. Munagi

Research output: Contribution to journalArticlepeer-review


Inspired by the results of Gelfand, Graev and Postnikov (1997) on the reduction rule for binary trees, we present several bijections on different types of reduction rules for plane trees such as symmetric k-ary trees, locally symmetric k-ary trees, symmetric even trees, symmetric noncrossing trees and Motzkin trees. We give the corresponding enumeration results, and prove the equidistribution of some classes of trees.

Original languageEnglish
Pages (from-to)215-230
Number of pages16
JournalUtilitas Mathematica
StatePublished - Mar 2010


  • Catalan numbers
  • Even trees
  • Motzkin numbers
  • Noncrossing trees
  • Reduction rules
  • Ternary trees
  • k-ary trees

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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