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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)

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.

Keywords

Word Length Covering Relation Fibonacci Number Lattice Path Binomial Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bacher, A., Bernini, A., Ferrari, L., Gunby, B., Pinzani, R., West, J.: The Dyck pattern poset. Discrete Math. 321, 12–23 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bernini, A., Ferrari, L., Pinzani, R., West, J.: Pattern avoiding Dyck paths. Discrete Math. Theoret. Comput. Sci. Proc. AS, 683–694 (2013)Google Scholar
  3. 3.
    Bilotta, S., Grazzini, E., Pergola, E., Pinzani, R.: Avoiding cross-bifix-free binary words. Acta Inform. 50, 157–173 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Björner, A.: The Möbius function of factor order. Theoret. Comput. Sci. 117, 91–98 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 3, 326–336 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Marcus, A., Tardos, G.: Excluded permutation matrices and the Stanley-Wilf conjecture. J. Combin. Theory Ser. A 107, 153–160 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, electronically available at oeis.org
  8. 8.
    Spielman, D.A., Bóna, M.: An infinite antichain of permutations. Electron. J. Combin. 7, 4 (2000). #N2Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

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

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