Modular flip-graphs of one-holed surfaces

被引：4

作者：

Parlier, Hugo ^{[1
]}

Pournin, Lionel ^{[2
]}

机构：

[1] Univ Luxembourg, Math Res Unit, Luxembourg, Luxembourg

[2] Univ Paris 13, LIPN, Villetaneuse, France

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2018年 / 67卷

基金：

瑞士国家科学基金会;

关键词：

D O I：

10.1016/j.ejc.2017.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus g with a single boundary curve and n marked points on this curve and consider triangulations up to homeomorphism with the marked points as their vertices. Our results are bounds on the maximal distance between two triangulations. Our lower bounds assert that these distances grow at least like 5n/2 for all g >= 1. Our upper bounds grow at most like [4 - 1/(4g)]n for g >= 2, and at most like 23n/8 for the bordered torus. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：158 / 173

页数：16

共 12 条

[1]

[Anonymous], 1988, J. Amer. Math. Soc., DOI DOI 10.2307/1990951.MR928904

[2]

Bose Prosenjit, 2012, Computational Geometry. XIV Spanish Meeting, EGC 2011. Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday. Revised Selected Papers, P29, DOI 10.1007/978-3-642-34191-5_3

[3]

De Loera J. A., 2010, ALGORITHMS COMPUTATI, V25

[4] THE GEOMETRY OF FLIP GRAPHS AND MAPPING CLASS GROUPS [J].

Disarlo, Valentina ;

Parlier, Hugo .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (06) :3809-3844

[5] ON THE IDEAL TRIANGULATION GRAPH OF A PUNCTURED SURFACE [J].

Korkmaz, Mustafa ;

Papadopoulos, Athanase .

ANNALES DE L INSTITUT FOURIER, 2012, 62 (04) :1367-1382

[6] THE ASSOCIAHEDRON AND TRIANGULATIONS OF THE N-GON [J].

LEE, CW .

EUROPEAN JOURNAL OF COMBINATORICS, 1989, 10 (06) :551-560

[7]

MOSHER L, 1988, T AM MATH SOC, V306, P1

[8] Flip-graph moduli spaces of filling surfaces [J].

Parlier, Hugo ;

Pournin, Lionel .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2017, 19 (09) :2697-2737

[9] The diameter of associahedra [J].

Pournin, Lionel .

ADVANCES IN MATHEMATICS, 2014, 259 :13-42

[10]

Stasheff J D., 1963, Trans. Am. Math. Soc, V108, P293

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