episciences.org_1322_1639048293
1639048293
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
07
21
2016
Vol. 18 no. 2, Permutation...
Permutation Patterns
Pattern avoidance in forests of binary shrubs
David
Bevan
Derek
Levin
Peter
Nugent
Jay
Pantone
Lara
Pudwell
Manda
Riehl
ML
Tlachac
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.
07
21
2016
1322
arXiv:1510.08036
10.46298/dmtcs.1322
https://dmtcs.episciences.org/1322