The expected genus of a random chord diagram
Geometric Topology
2009-04-29 v1 Combinatorics
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).
Keywords
Cite
@article{arxiv.0904.4361,
title = {The expected genus of a random chord diagram},
author = {Nathan Linial and Tahl Nowik},
journal= {arXiv preprint arXiv:0904.4361},
year = {2009}
}