Pattern avoidance in forests of binary shrubs

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

Research output: Contribution to journalArticle

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Abstract

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.
LanguageEnglish
Number of pages22
JournalDiscrete Mathematics and Theoretical Computer Science
Volume18
Issue number2
StatePublished - 21 Jul 2016

Keywords

  • pattern avoidance
  • permutation patterns
  • linear extensions

Cite this

Bevan, D., Levin, D., Nugent, P., Pantone, J., Pudwell, L., Riehl, M., & Tlachac, ML. (2016). Pattern avoidance in forests of binary shrubs. Discrete Mathematics and Theoretical Computer Science, 18(2).
Bevan, David ; Levin, Derek ; Nugent, Peter ; Pantone, Jay ; Pudwell, Lara ; Riehl, Manda ; Tlachac, ML. / Pattern avoidance in forests of binary shrubs. In: Discrete Mathematics and Theoretical Computer Science. 2016 ; Vol. 18, No. 2.
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Bevan, D, Levin, D, Nugent, P, Pantone, J, Pudwell, L, Riehl, M & Tlachac, ML 2016, 'Pattern avoidance in forests of binary shrubs' Discrete Mathematics and Theoretical Computer Science, vol. 18, no. 2.

Pattern avoidance in forests of binary shrubs. / Bevan, David; Levin, Derek; Nugent, Peter; Pantone, Jay; Pudwell, Lara; Riehl, Manda; Tlachac, ML.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 18, No. 2, 21.07.2016.

Research output: Contribution to journalArticle

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AU - Tlachac,ML

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Bevan D, Levin D, Nugent P, Pantone J, Pudwell L, Riehl M et al. Pattern avoidance in forests of binary shrubs. Discrete Mathematics and Theoretical Computer Science. 2016 Jul 21;18(2).