Journal of Integer Sequences, Vol. 24 (2021), Article 21.1.3

Schröder Coloring and Applications

Daniel Birmajer
Nazareth College
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.

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(Concerned with sequences A000079 A001003 A006318 A064062 A108524 A151374 A153231 A217360 A217364.)

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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