Permutations Restricted by Two Distinct Patterns of Length Three

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Define Sₙ(R;T) to be the number of permutations on n letters which avoid all patterns in the set R and contain each pattern in the multiset T exactly once. In this paper we enumerate Sₙ({α};{β}) and Sₙ(;{α,β}) for all α≠ β∈ S₃. The results for Sₙ({α};{β}) follow from two papers by Mansour and Vainshtein.