Enumerative Results on the Schroeder Pattern Poset

摘要

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