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

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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.
Original languageEnglish
Pages (from-to)3–20
Number of pages18
JournalAustralasian Journal of Combinatorics
Publication statusPublished - 29 Feb 2016


  • permutation classes
  • kernel method
  • Hasse graphs


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