Enumeration of permutations with forbidden templates
For any permutation σ of k letters, a permutation π avoids σ iff there is no number i with 0 < i < n − 1 such that [π(i), π( i + 1), [special characters omitted], π(i + k − 1)] is order-isomorphic to [σ(1), σ(2), [special characters omitted], σ(k)]. In other words, there is no continuous subsequence of π of length k such that it has the same pairwise comparisons of letters as σ. We will call σ a template and A(σ, n) will be the number of permutations in Sn which forbids the template σ. We find the cardinality of A(σ, n) for various σ as well as for some sets of σ's. We also establish the recurrence structure of A(σ, n) and find the upper bound and lower bound of A(σ, n) for σ with a certain length.
Zhang, Yuang-Sheng, "Enumeration of permutations with forbidden templates" (2001). Dissertations available from ProQuest. AAI3003715.