The Expected Genus of a Random Chord Diagram

Nathan Linial, Tahl Nowik*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 <c2 and n0 such that c1 In n ≤ n/2 - sn ≤ c2 In n for all n ≥ n0.

Original languageAmerican English
Pages (from-to)161-180
Number of pages20
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jan 2011


  • Curves in surfaces
  • Gauss code


Dive into the research topics of 'The Expected Genus of a Random Chord Diagram'. Together they form a unique fingerprint.

Cite this