The Expected Genus of a Random Chord Diagram

Nathan Linial, Tahl Nowik

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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

Original languageEnglish
Pages (from-to)161-180
Number of pages20
JournalDiscrete and Computational Geometry
Volume45
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Curves in surfaces
  • Gauss code

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