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Pattern-avoiding involutions: exact and asymptotic enumeration. (English) Zbl 1333.05018

Summary: We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. We directly enumerate the involutions avoiding 1342 and the involutions avoiding 2341. As we demonstrate, the numerical data for these problems exhibits some surprising behavior. This strange behavior even provides some very unexpected data related to the number of 1324-avoiding permutations.

MSC:

05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration

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Online Encyclopedia of Integer Sequences:

The number of 123-avoiding simple involutions of length n.