132-avoiding permutations with an adjacency bound |π_{i+1}-π_i|≤m admit a structural collapse on the position of n; for m=2 this yields explicit recurrences, a rational generating function, and asymptotic growth A_n^{(2)} ∼ C α^n with α≈1.4656.
CRC Press, 2 edition, 2012
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On 132-Avoiding Permutations with an Adjacency Constraint
132-avoiding permutations with an adjacency bound |π_{i+1}-π_i|≤m admit a structural collapse on the position of n; for m=2 this yields explicit recurrences, a rational generating function, and asymptotic growth A_n^{(2)} ∼ C α^n with α≈1.4656.