Author:
Cioni Lapo,Ferrari Luca,Henriet Corentin
Abstract
We define a bijection between \emph{two-stack sortable permutations} and \emph{fighting fish}, enriching the garden of bijections linking the numerous combinatorial classes counted by the sequence $A000139$ of the OEIS. Our bijection is (up to symmetry) the non-recursive version of the one of Fang (2018). Along the way, we encounter \emph{labeled sorting trees}, a new class of trees that appear to have nice properties that seem worth to explore.
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