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.
|Number of pages||22|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|Publication status||Published - 21 Jul 2016|
- pattern avoidance
- permutation patterns
- linear extensions