Pattern avoidance in forests of binary shrubs

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 avoidin...

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Bibliographic Details
Published inDiscrete Mathematics and Theoretical Computer Science Vol. 18; no. 2; p. F1
Main Authors Bevan, David, Levin, Derek, Nugent, Peter, Pantone, Jay, Pudwell, Lara, Riehl, Manda, Tlachac, ML
Format Journal Article
LanguageEnglish
Published Nancy DMTCS 01.06.2016
Subjects
Avoidance
Combinatorial analysis
Forests
Machinery
Mathematical research
Permutations
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Summary: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=ℓxy=ℓx, for some ℓ∈Q+ℓ∈Q+, one of these being the celebrated Duchon's club paths with ℓ=2/3ℓ=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.
ISSN:1462-7264
1365-8050