Schröder parenthesizations and chordates

Richard Ehrenborg, Miguel Mendez

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We establish that Schroder trees are a subclass of Schröder parenthesizations by a natural bijection. The Haiman-Schmitt bijection between Schröder parenthesizations, enriched by uniform species and partitions, generalizes to a bijection between Schröder parenthesizations and assemblies. Using these bijections, we prove some tree counting formulas. We also introduce the definitions of trees over a partition and similarly chordates over a partition. These structures give rise to some beautiful enumeration formulas.

Original languageEnglish
Pages (from-to)127-139
Number of pages13
JournalJournal of Combinatorial Theory. Series A
Issue number2
StatePublished - Aug 1994

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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