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The absence of a pattern and the occurrences of another

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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Miklós Bóna. The absence of a pattern and the occurrences of another. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, Vol. 12 no. 2 (2), pp.89-102. ⟨10.46298/dmtcs.496⟩. ⟨hal-00990453⟩

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