Discrete Mathematics & Theoretical Computer Science, Vol 12, No 2 (2010)

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The absence of a pattern and the occurrences of another

Miklos Bona

Abstract


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.

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