We define a bijection between two-stack sortable permutations and 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 labeled sorting trees, a new class of trees that appear to have nice properties that seem worth to explore.
A direct bijection between two-stack sortable permutations and fighting fish / Cioni, Lapo; Ferrari, Luca; Henriet, Corentin. - ELETTRONICO. - (2023), pp. 283-289. (Intervento presentato al convegno 12th European Conference on Combinatorics, Graph Theory and Applications tenutosi a Prague nel 28 agosto - 1 settembre 2023) [10.5817/CZ.MUNI.EUROCOMB23-039].
A direct bijection between two-stack sortable permutations and fighting fish
Cioni, Lapo;Ferrari, Luca;Henriet, Corentin
2023
Abstract
We define a bijection between two-stack sortable permutations and 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 labeled sorting trees, a new class of trees that appear to have nice properties that seem worth to explore.
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