The permutation classes Av(1234,2341) and Av(1243,2314)

Bevan, David (2016) The permutation classes Av(1234,2341) and Av(1243,2314). Australasian Journal of Combinatorics, 64. 3–20. ISSN 1034-4942

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    Abstract

    We investigate the structure of the two permutation classes defined by the sets of forbidden patterns {1234, 2341} and {1243, 2314}. By considering how the Hasse graphs of permutations in these classes can be built from a sequence of rooted source graphs, we determine their algebraic generating functions. Our approach is similar to that of “adding a slice”, used previously to enumerate various classes of polyominoes and other combinatorial structures. To solve the relevant functional equations, we make extensive use of the kernel method.

    ORCID iDs

    Bevan, David ORCID logoORCID: https://orcid.org/0000-0001-7179-2285;