Geodesic
Pattern avoidance in forests of binary shrubs
Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2.

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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 $y=\ell x$, for some $\ell\in\mathbb{Q}^+$, one of these being the celebrated Duchon's club paths with $\ell=2/3$. 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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     author = {Bevan, David and Levin, Derek and Nugent, Peter and Pantone, Jay and Pudwell, Lara and Riehl, Manda and Tlachac, ML},
     title = {Pattern avoidance in forests of binary shrubs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     number = {2},
     year = {2015-2016},
     doi = {10.46298/dmtcs.1322},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1322/}
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Bevan, David; Levin, Derek; Nugent, Peter; Pantone, Jay; Pudwell, Lara; Riehl, Manda; Tlachac, ML. Pattern avoidance in forests of binary shrubs. Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2. doi : 10.46298/dmtcs.1322. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1322/

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