### 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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