Skip to Main content Skip to Navigation
Conference papers

Pattern avoidance in partial permutations (extended abstract)

Abstract : Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A $\textit{partial permutation of length n with k holes}$ is a sequence of symbols $\pi = \pi_1 \pi_2 \cdots \pi_n$ in which each of the symbols from the set $\{1,2,\ldots,n-k\}$ appears exactly once, while the remaining $k$ symbols of $\pi$ 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 $n \geq k \geq 1$.
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 24, 2015 - 3:44:42 PM
Last modification on : Monday, August 24, 2020 - 3:42:06 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 4:43:35 PM


Publisher files allowed on an open archive




Anders Claesson, Vít Jelínek, Eva Jelínková, Sergey Kitaev. Pattern avoidance in partial permutations (extended abstract). 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.625-636, ⟨10.46298/dmtcs.2818⟩. ⟨hal-01186246⟩



Record views


Files downloads