10.46298/dmtcs.1322
Bevan, David
David
Bevan
Levin, Derek
Derek
Levin
Nugent, Peter
Peter
Nugent
Pantone, Jay
Jay
Pantone
Pudwell, Lara
Lara
Pudwell
Riehl, Manda
Manda
Riehl
Tlachac, ML
ML
Tlachac
Pattern avoidance in forests of binary shrubs
episciences.org
2016
Mathematics - Combinatorics
contact@episciences.org
episciences.org
2016-07-21T04:22:47+02:00
2021-08-23T23:09:19+02:00
2016-07-21
eng
Journal article
https://dmtcs.episciences.org/1322
arXiv:1510.08036
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; Vol. 18 no. 2, Permutation Patterns 2015 ; Permutation Patterns ; 1365-8050
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.