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Enumerative Results on the Schröder Pattern Poset

Abstract : 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.
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Lapo Cioni, Luca Ferrari. Enumerative Results on the Schröder Pattern Poset. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.56-67, ⟨10.1007/978-3-319-58631-1_5⟩. ⟨hal-01656348⟩

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