Fighting Fish and Two-Stack Sortable Permutations

Wenjie Fang

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung


In 2017, Duchi, Guerrini, Rinaldi and Schaeffer proposed new 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, we also prove the algebraicity of a generating function of two-stack sortable permutations, extending a result of Bousquet-Mélou (1998).
TitelSéminaire Lotharingien de Combinatoire
UntertitelProceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics"
Herausgeber (Verlag)European Mathematical Society
ISBN (elektronisch)1286-4889
PublikationsstatusVeröffentlicht - 1 Apr. 2018
VeranstaltungThe 30th International Conference on Formal Power Series and Algebraic Combinatorics - Dartmouth college, Hanover, USA / Vereinigte Staaten
Dauer: 16 Juli 201820 Juli 2018


KonferenzThe 30th International Conference on Formal Power Series and Algebraic Combinatorics
KurztitelFPSAC 2018
Land/GebietUSA / Vereinigte Staaten


Untersuchen Sie die Forschungsthemen von „Fighting Fish and Two-Stack Sortable Permutations“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren