Pattern avoidance in forests of binary shrubs

David Bevan, Derek Levin, Peter Nugent, Jay Pantone, Lara Pudwell, Manda Riehl, ML Tlachac

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2 Citations (Scopus)
74 Downloads (Pure)


We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary shrub forests. In this context, we enumerate forests avoiding patterns of length three. In four of the five non-equivalent cases, we present explicit enumerations by exhibiting bijections with certain lattice paths bounded above by the line y = ℓx , for some ℓ ∈ Q+ , one of these being the celebrated Duchon’s club paths with ℓ = 2/3. In the remaining case, we use the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate.
Original languageEnglish
Number of pages22
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number2
Publication statusPublished - 21 Jul 2016


  • pattern avoidance
  • permutation patterns
  • linear extensions


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