Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Pattern avoidance in inversion sequences

Pattern avoidance in inversion sequences Abstract A permutation of length n may be represented, equivalently, by a sequence a 1 a 2 • • • a n satisfying 0 < a i < i for all z, which is called an inversion sequence. In analogy to the usual case for permutations, the pattern avoidance question is addressed for inversion sequences. In particular, explicit formulas and/or generating functions are derived which count the inversion sequences of a given length that avoid a single pattern of length three. Among the sequences encountered are the Fibonacci numbers, the Schröder numbers, and entry A200753 in OEIS. We make use of both algebraic and combinatorial methods to establish our results. An explicit Injection is given between two of the avoidance classes, and in three cases, the kernel method is used to solve a functional equation satisfied by the generating function enumerating the class in question. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure Mathematics and Applications de Gruyter

Pattern avoidance in inversion sequences

Download PDF
20 pages

Loading next page...
 
/lp/de-gruyter/pattern-avoidance-in-inversion-sequences-aP9IVFYHqs
Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1788-800X
eISSN
1788-800X
DOI
10.1515/puma-2015-0016
Publisher site
See Article on Publisher Site

Abstract

Abstract A permutation of length n may be represented, equivalently, by a sequence a 1 a 2 • • • a n satisfying 0 < a i < i for all z, which is called an inversion sequence. In analogy to the usual case for permutations, the pattern avoidance question is addressed for inversion sequences. In particular, explicit formulas and/or generating functions are derived which count the inversion sequences of a given length that avoid a single pattern of length three. Among the sequences encountered are the Fibonacci numbers, the Schröder numbers, and entry A200753 in OEIS. We make use of both algebraic and combinatorial methods to establish our results. An explicit Injection is given between two of the avoidance classes, and in three cases, the kernel method is used to solve a functional equation satisfied by the generating function enumerating the class in question.

Journal

Pure Mathematics and Applications – de Gruyter

Published: Dec 1, 2015

References

  • Restricted avoiding ary words Chebyshev polynomials continued fractions in
    Mansour
  • Burstein Enumeration of Words with Forbidden Patterns Ph thesis University of Pennsylvania
  • inversion sequences and partitions of type at http arxiv org abs
    Chen
  • Pattern avoidance in flattened partitions
    Callan
  • series of lecture hall polytopes and Eulerian polynomials for inversion sequences Theory
    Savage
  • Enumeration schemes and more importantly their automatic generation
    Zeilberger
  • The On - Line Encyclopedia of Integer Sequences at http oeis org
    Sloane
  • Kernel method and systems of functional equations with several conditions
    Hou
  • Burstein Enumeration of Words with Forbidden Patterns Ph thesis University of Pennsylvania
  • Enumeration schemes and more importantly their automatic generation
    Zeilberger
  • series of lecture hall polytopes and Eulerian polynomials for inversion sequences Theory
    Savage