Pattern avoidance in forests of binary shrubs

Bevan, David; Levin, Derek; Nugent, Peter; Pantone, Jay; Pudwell, Lara; Riehl, Manda and Tlachac, ML (2016). Pattern avoidance in forests of binary shrubs. Discrete Mathematics and Theoretical Computer Science, 18(2), article no. 8.

URL: http://dmtcs.episciences.org/1541/pdf

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 in 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.

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