Publication at Faculty of Mathematics and Physics |
2010
Abstract
A partial permutation of length n with k holes is a sequence of symbols in which each of the symbols from the set {1,2,...,n-k} appears exactly once, while the remaining symbols are "holes". We define 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 partial permutations with k holes avoiding a given pattern of length at most four.