Counting recurrences for the permutation classes Av(1342) and Av(12453)
For a permutation pattern τ, let Av_n(τ) be the set of permutations of length n that avoid τ. This formalization proves, for every n, that four recurrences from the source paper compute |Av_n(1342)| and |Av_n(12453)|. For 1342 they are the one-threshold recurrence W and the scalar kernel recurrence G, and for 12453 the literal two-threshold recurrence H and the transfer-kernel recurrence G. These are the cases d = 1 and d = 2 of the paper's counting recurrences for the classes Av(12...d ⊕ 231), the direct sum of an increasing pattern and 231, whose kernel form gives polynomial-time…
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