The Expected Genus of a Random Chord Diagram

Nathan Linial; Tahl Nowik

doi:https://doi.org/10.1007/s00454-010-9276-x

The Expected Genus of a Random Chord Diagram

Nathan Linial, Tahl Nowik

The Hebrew University of Jerusalem, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let g_n denote the expected genus of a randomly chosen oriented chord diagram of order n. We show that g_n satisfies, I.e., there exist 0 < c₁ <c₂ and n₀ such that c₁ In n ≤ n/2 - s_n ≤ c₂ In n for all n ≥ n₀.

Original language	English
Pages (from-to)	161-180
Number of pages	20
Journal	Discrete and Computational Geometry
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s00454-010-9276-x
State	Published - Jan 2011

Keywords

Curves in surfaces
Gauss code

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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abstract = "To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let gn denote the expected genus of a randomly chosen oriented chord diagram of order n. We show that gn satisfies, I.e., there exist 0 < c1 2 and n0 such that c1 In n ≤ n/2 - sn ≤ c2 In n for all n ≥ n0.",

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AB - To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let gn denote the expected genus of a randomly chosen oriented chord diagram of order n. We show that gn satisfies, I.e., there exist 0 < c1 2 and n0 such that c1 In n ≤ n/2 - sn ≤ c2 In n for all n ≥ n0.

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 1

ER -

The Expected Genus of a Random Chord Diagram

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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