Enumerative Results on the Schröder Pattern Poset

  • Lapo Cioni
  • Luca FerrariEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)


The set of Schröder words (Schröder language) is endowed with a natural partial order, which can be conveniently described by interpreting Schröder words as lattice paths. The resulting poset is called the Schröder pattern poset. We find closed formulas for the number of Schröder words covering/covered by a given Schröder word in terms of classical parameters of the associated Schröder path. We also enumerate several classes of Schröder avoiding words (with respect to the length), i.e. sets of Schröder words which do not contain a given Schröder word.


Word Length Covering Relation Fibonacci Number Lattice Path Binomial Coefficient 
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Authors and Affiliations

  1. 1.Dipartimento di Matematica e Informatica “U. Dini”University of FirenzeFirenzeItaly

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