Non-leaving-face property for marked surfaces

被引：2

作者：

Brustle, Thomas ^{[1
]}

Zhang, Jie ^{[2
]}

机构：

[1] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2019年 / 14卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Marked surface; non-leaving-face property; exchange graph; 13F60; 13E10; 16G20; CLUSTER ALGEBRAS; ASSOCIAHEDRA; DIAMETER;

D O I：

10.1007/s11464-019-0767-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the polytope arising from a marked surface by flips of triangulations. D. D. Sleator, R. E. Tarjan, and W. P. Thurston [J. Amer. Math. Soc., 1988, 1(3): 647-681] studied the diameter of the associahedron, which is the polytope arising from a marked disc by flips of triangulations. They showed that every shortest path between two vertices in a face does not leave that face. We give a new method, which is different from the one used by V. Disarlo and H. Parlier [arXiv: 1411.4285] to establish the same non-leaving-face property for all unpunctured marked surfaces.

引用

页码：521 / 534

页数：14

共 20 条

[1]

Brüsde T, 2013, EMS SER CONGR REP, P135

[2] Tagged mapping class groups: Auslander-Reiten translation [J].

Bruestle, Thomas ;

Qiu, Yu .

MATHEMATISCHE ZEITSCHRIFT, 2015, 279 (3-4) :1103-1120

[3] A MODULE-THEORETIC INTERPRETATION OF SCHIFFLER'S EXPANSION FORMULA [J].

Bruestle, Thomas ;

Zhang, Jie .

COMMUNICATIONS IN ALGEBRA, 2013, 41 (01) :260-283

[4]

Brüstle T, 2011, ALGEBR NUMBER THEORY, V5, P529

[5] Tilting theory and cluster combinatorics [J].

Buan, Aslak Bakke ;

Marsh, Bethany Rose ;

Reineke, Markus ;

Reiten, Idun ;

Todorov, Gordana .

ADVANCES IN MATHEMATICS, 2006, 204 (02) :572-618

[6] The diameter of type D associahedra and the non-leaving-face property [J].

Ceballos, Cesar ;

Pilaud, Vincent .

EUROPEAN JOURNAL OF COMBINATORICS, 2016, 51 :109-124

[7] Polytopal realizations of generalized associahedra [J].

Chapoton, F ;

Fomin, S ;

Zelevinsky, A .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2002, 45 (04) :537-566

[8]

Disarlo V, ARXIV 1411 4285

[9] Cluster algebras II: Finite type classification [J].

Fomin, S ;

Zelevinsky, A .

INVENTIONES MATHEMATICAE, 2003, 154 (01) :63-121

[10] Cluster algebras I: Foundations [J].

Fomin, S ;

Zelevinsky, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (02) :497-529

← 1 2 →