Computational approaches to consecutive pattern avoidance in permutations In recent years, there has been increasing interest in consecutive pattern avoidance in permutations. In this paper, we introduce two approaches to counting permutations that avoid a set of prescribed patterns consecutively. These algorithms have been implemented in the accompanying Maple package CAV, which can be downloaded from the author’s website. As a byproduct of the first algorithm, we have a theorem giving a sufficient condition for when two pattern sets are strongly (consecutively) Wilf-equivalent. For the implementation of the second algorithm, we define the cluster tail generating function and show that it always satisfies a certain functional equation. We also explain how the CAV package can be used to approximate asymptotic constants for single pattern avoidance.
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References in zbMATH (referenced in 11 articles , 1 standard article )
Showing results 1 to 11 of 11.
- Yang, Mingjia; Zeilberger, Doron: Increasing consecutive patterns in words (2020)
- Auli, Juan S.; Elizalde, Sergi: Consecutive patterns in inversion sequences. II: Avoiding patterns of relations (2019)
- Lee, Mitchell; Sah, Ashwin: Constraining strong (c)-Wilf equivalence using cluster poset asymptotics (2019)
- Dwyer, Tim; Elizalde, Sergi: Wilf equivalence relations for consecutive patterns (2018)
- Baxter, Andrew; Nakamura, Brian; Zeilberger, Doron: Automatic generation of theorems and proofs on enumerating consecutive-Wilf classes (2013)
- Dotsenko, Vladimir; Khoroshkin, Anton: Shuffle algebras, homology, and consecutive pattern avoidance (2013)
- Elizalde, Sergi: The most and the least avoided consecutive patterns (2013)
- Perarnau, Guillem: A probabilistic approach to consecutive pattern avoiding in permutations (2013)
- Dotsenko, Vladimir: Pattern avoidance in labelled trees (2012)
- Elizalde, Sergi; Noy, Marc: Clusters, generating functions and asymptotics for consecutive patterns in permutations (2012)
- Nakamura, Brian: Computational approaches to consecutive pattern avoidance in permutations (2011)