# Permutations all of whose patterns of a given length are distinct Journal article, 2013

For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \sigma \in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3} \rfloor + e_k, where e_k \in {-1,0} for every k. We conjecture an even more precise result, based on data for small values of k.

Tilted checkerboard permutation

Permutation pattern

k-Separator

## Author

#### Peter Hegarty

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

#### Journal of Combinatorial Theory - Series A

0097-3165 (ISSN)

Vol. 120 7 1663-1671

Basic sciences

#### Subject Categories

Discrete Mathematics

#### DOI

10.1016/j.jcta.2013.06.006