31 research outputs found
Pattern-Avoiding Involutions: Exact and Asymptotic Enumeration
We consider the enumeration of pattern-avoiding involutions, focusing in
particular on sets defined by avoiding a single pattern of length 4. As we
demonstrate, the numerical data for these problems demonstrates some surprising
behavior. This strange behavior even provides some very unexpected data related
to the number of 1324-avoiding permutations
Pattern avoiding alternating involutions
We enumerate and characterize some classes of alternating and reverse
alternating involutions avoiding a single pattern of length three or four. If
on one hand the case of patterns of length three is trivial, on the other hand,
the length four case is more challenging and involves sequences of
combinatorial interest, such as Motzkin and Fibonacci numbers