### Abstract

Original language | English |
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Pages | 625-636 |

Number of pages | 12 |

Publication status | Published - 2010 |

Event | 22nd International Conference on Formal Power Series & Algebraic Combinatorics - San Francisco State University, San Francisco, United States Duration: 2 Aug 2010 → 6 Aug 2010 |

### Conference

Conference | 22nd International Conference on Formal Power Series & Algebraic Combinatorics |
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Country | United States |

City | San Francisco |

Period | 2/08/10 → 6/08/10 |

### Fingerprint

### Keywords

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

### Cite this

*Pattern avoidance in partial permutations*. 625-636. Poster session presented at 22nd International Conference on Formal Power Series & Algebraic Combinatorics, San Francisco, United States.

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

Research output: Contribution to conference › Poster

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 -