Séminaire Lotharingien de Combinatoire, 86B.83 (2022), 12 pp.

Enrica Duchi and Corentin Henriet

Bijections Between Fighting Fish, Planar Maps, and Tamari Intervals

Abstract. We introduce two models of classes of walks in the quarter plane defined by simple rewriting rules: generalized fighting fish and extended fighting fish. They are two generalizations in different directions of the recently introduced fighting fish of (Duchi, Guerrini, Rinaldi, Schaeffer 2017), that were shown to be equinumerated with rooted non-separable planar maps and synchronized Tamari intervals. We explain these equinumeration results by presenting two direct and more general bijections: one between generalized fighting fish and rooted planar maps, and the other between extended fighting fish and Tamari intervals.


Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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