# 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

, Volume 25 (2) – Dec 1, 2015
20 pages

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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 Applicationsde Gruyter

Published: Dec 1, 2015

### References

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