Fighting Fish and Two-Stack Sortable Permutations

Wenjie Fang

Fighting Fish and Two-Stack Sortable Permutations

Wenjie Fang

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Abstract

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).

Originalsprache	englisch
Titel	Séminaire Lotharingien de Combinatoire
Untertitel	Proceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics"
Herausgeber (Verlag)	European Mathematical Society
Seitenumfang	12
Band	80B
ISBN (elektronisch)	1286-4889
Publikationsstatus	Veröffentlicht - 1 Apr. 2018
Veranstaltung	The 30th International Conference on Formal Power Series and Algebraic Combinatorics - Dartmouth college, Hanover, USA / Vereinigte Staaten Dauer: 16 Juli 2018 → 20 Juli 2018 https://sites.google.com/view/fpsac2018/home

Konferenz

Konferenz	The 30th International Conference on Formal Power Series and Algebraic Combinatorics
Kurztitel	FPSAC 2018
Land/Gebiet	USA / Vereinigte Staaten
Ort	Hanover
Zeitraum	16/07/18 → 20/07/18
Internetadresse	https://sites.google.com/view/fpsac2018/home

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Fang, W 2018, Fighting Fish and Two-Stack Sortable Permutations. in Séminaire Lotharingien de Combinatoire: Proceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics". Bd. 80B, 7, European Mathematical Society, The 30th International Conference on Formal Power Series and Algebraic Combinatorics, Hanover, New Hampshire, USA / Vereinigte Staaten, 16/07/18. <https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2018/07-Fang.html>

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title = "Fighting Fish and Two-Stack Sortable Permutations",

abstract = " 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-M{\'e}lou (1998).",

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T1 - Fighting Fish and Two-Stack Sortable Permutations

AU - Fang, Wenjie

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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).

AB - 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).

KW - two-stack sortable permutations

KW - fighting fish

KW - bijection

KW - recursive decomposition

M3 - Conference paper

VL - 80B

BT - Séminaire Lotharingien de Combinatoire

PB - European Mathematical Society

T2 - The 30th International Conference on Formal Power Series and Algebraic Combinatorics

Y2 - 16 July 2018 through 20 July 2018

ER -

Fighting Fish and Two-Stack Sortable Permutations

Abstract

Konferenz

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