Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

Pattern avoidance in partial permutations

Claesson, Anders and Jelínek, Vit and Jelinkova, Eva and Kitaev, Sergey (2010) Pattern avoidance in partial permutations. In: 22nd International Conference on Formal Power Series & Algebraic Combinatorics, 2010-08-02 - 2010-08-06, San Francisco State University.

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols π=π1π2⋯πn in which each of the symbols from the set {1,2,…,n-k} appears exactly once, while the remaining k symbols of π are ``holes''. We introduce pattern-avoidance in partial permutations and prove that most of the previous results on Wilf equivalence of permutation patterns can be extended to partial permutations with an arbitrary number of holes. We also show that Baxter permutations of a given length k correspond to a Wilf-type equivalence class with respect to partial permutations with (k-2) holes. Lastly, we enumerate the partial permutations of length n with k holes avoiding a given pattern of length at most four, for each n≥k≥1.