The absence of a pattern and the number of occurrences of another

Details The absence of a pattern and the number of occurrences of another The absence of a pattern and the number of occurrences of another

2009-10-07

arxiv.org/abs/0910.1343v1

Mathematics

Combinatorics

16 pages, 3 figures

Scientific paper

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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