Pattern avoidance in partial permutations

Anders Claesson, Vit Jelínek, Eva Jelinkova, Sergey Kitaev

Research output: Contribution to conferencePoster

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.
Original languageEnglish
Pages625-636
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

Conference

Conference22nd International Conference on Formal Power Series & Algebraic Combinatorics
CountryUnited States
CitySan Francisco
Period2/08/106/08/10

Fingerprint

Pattern Avoidance
Permutation
Partial
Partial Words
Equivalence class
Equivalence

Keywords

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

Cite this

Claesson, A., Jelínek, V., Jelinkova, E., & Kitaev, S. (2010). Pattern avoidance in partial permutations. 625-636. Poster session presented at 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States.
Claesson, Anders ; Jelínek, Vit ; Jelinkova, Eva ; Kitaev, Sergey. / Pattern avoidance in partial permutations. Poster session presented at 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States.12 p.
@conference{25e46e99838c472eb6705e2cf19daee5,
title = "Pattern avoidance in partial permutations",
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.",
keywords = "partial permutation, pattern avoidance, bijection, generating function, Baxter permutation",
author = "Anders Claesson and Vit Jel{\'i}nek and Eva Jelinkova and Sergey Kitaev",
year = "2010",
language = "English",
pages = "625--636",
note = "22nd International Conference on Formal Power Series & Algebraic Combinatorics ; Conference date: 02-08-2010 Through 06-08-2010",

}

Claesson, A, Jelínek, V, Jelinkova, E & Kitaev, S 2010, 'Pattern avoidance in partial permutations' 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States, 2/08/10 - 6/08/10, pp. 625-636.

Pattern avoidance in partial permutations. / Claesson, Anders; Jelínek, Vit; Jelinkova, Eva; Kitaev, Sergey.

2010. 625-636 Poster session presented at 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States.

Research output: Contribution to conferencePoster

TY - CONF

T1 - Pattern avoidance in partial permutations

AU - Claesson, Anders

AU - Jelínek, Vit

AU - Jelinkova, Eva

AU - Kitaev, Sergey

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - partial permutation

KW - pattern avoidance

KW - bijection

KW - generating function

KW - Baxter permutation

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAN0143

M3 - Poster

SP - 625

EP - 636

ER -

Claesson A, Jelínek V, Jelinkova E, Kitaev S. Pattern avoidance in partial permutations. 2010. Poster session presented at 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States.