The expected genus of a random chord diagram

2009/04/28 by Nathan Linial, Linial, Nathan, Tahl Nowik +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0904.4361

openalex publication_date 2009/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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: g_n = n/2 - Theta(ln n).

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