Pattern avoidance in partial permutations

Anders Claesson, Vit Jelínek, Eva Jelinkova, Sergey Kitaev

Research output: Contribution to conferencePosterpeer-review


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.
Original languageEnglish
Number of pages12
Publication statusPublished - 2010
Event22nd International Conference on Formal Power Series & Algebraic Combinatorics - San Francisco State University, San Francisco, United States
Duration: 2 Aug 20106 Aug 2010


Conference22nd International Conference on Formal Power Series & Algebraic Combinatorics
Country/TerritoryUnited States
CitySan Francisco


  • partial permutation
  • pattern avoidance
  • bijection
  • generating function
  • Baxter permutation


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