The average genus of oriented rational links with a given crossing number

2022/04/26 by Dawn Ray, Ray, Dawn, Yuanan Diao +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 57K10 #Secondary: 57K31 #math.GT #msc:57K10 #msc:57K31

paper · pdf · doi:10.48550/arxiv.2204.12538

11 pages, 9 figures, 3 tables

arxiv created 2022/04/26 · arxiv updated 2022/04/28

Abstract

In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus. This allows us to obtain a precise formula for the average minimal genus of oriented rational knots and links with any given crossing number.

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