Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern q in permutations that avoid another given pattern r. In some cases, we find the pattern that occurs least often, (resp. most often) in all r-avoiding permutations. We also prove a few exact enumeration formulae, some of which are surprising.

Source : oai:HAL:hal-00990453v1

Volume: Vol. 12 no. 2

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: Permutation pattern,generating functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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