Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps

  title={Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps},
  author={Mikl{\'o}s B{\'o}na},
  journal={J. Comb. Theory, Ser. A},
Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342-avoiding permutations of length n as well as an exact formula for their number Sn(1342). While achieving this, we bijectively prove that the number of indecomposable 1342avoiding permutations of length n equals that of labeled plane trees of a certain type on n vertices recently enumerated by Cori, Jacquard and Schaeffer, which is in turn known to be… CONTINUE READING
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