Fighting fish and two-stack sortable permutations - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2018

Fighting fish and two-stack sortable permutations

Wenjie Fang

Résumé

In 2017, Duchi, Guerrini, Rinaldi and Schaeffer proposed a new family of combinatorial objects called "fighting fish", which are counted by the same formula as more classical objects, such as two-stack sortable permutations and non-separable planar maps. In this article, we explore the bijective aspect of fighting fish by establishing a bijection to two-stack sortable permutations, using a new recursive decomposition of these permutations. With our bijection, we give combinatorial explanations of several results on fighting fish proved previously with generating functions. Using the decomposition of two-stack sortable permutations, we also prove the algebraicity of their generating function, extending a result of Bousquet-M\'elou (1998).

Dates et versions

hal-02338108 , version 1 (29-10-2019)

Identifiants

Citer

Wenjie Fang. Fighting fish and two-stack sortable permutations. The 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2018), Jul 2018, Hanover, United States. ⟨hal-02338108⟩

Collections

INSMI
20 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More