Schröder Coloring and Applications
Rochester, NY 14618
Juan D. Gil
Massachusetts Institute of Technology
Cambridge, MA 02139
Juan B. Gil and Michael D. Weiner
Penn State Altoona
Altoona, PA 16601
We present several bijections, in terms of combinatorial objects counted
by the Schröder numbers, that are then used (via coloring of Dyck
paths) for the construction and enumeration of rational Schröder paths
with integer slope, ordered rooted trees, and simple rooted outerplanar
maps. On the other hand, we derive partial Bell polynomial identities
for the little and large Schröder numbers, which allow us to obtain
explicit enumeration formulas.
Full version: pdf,
(Concerned with sequences
Received August 4 2019; revised version received December 23 2019; December 24 2019; December 21 2020.
Published in Journal of Integer Sequences,
December 29 2020.
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