35 citations · 57 across the 24 of their papers we have counts for
24 papers
The Braid Indices of Pretzel Links: A Comprehensive Study, Part II
Yuanan Diao, Claus Ernst, Gabor Hetyei
This paper is the second part of our comprehensive study on the braid index problem of pretzel links. Our ultimate goal is to completely determine the braid indices of all pretzel…
The Braid Indices of Pretzel Links: A Comprehensive Study, Part I
Yuanan Diao, Claus Ernst, Gabor Hetyei
The determination of the braid index of an oriented link is generally a hard problem. In the case of alternating links, some significant progresses have been made in recent years w…
The Braid Indices of the Reverse Parallel Links of Alternating Knots
Yuanan Diao, Hugh Morton
The braid indices of most links remain unknown as there is no known universal method that can be used to determine the braid index of an arbitrary knot. This is also the case for a…
The ropelength conjecture of alternating knots
Yuanan Diao
A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true.…
The average genus of oriented rational links with a given crossing number
Dawn Ray, Yuanan Diao
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 obta…
Knots with equal bridge index and braid index
Yuanan Diao, Claus Ernst, Philipp Reiter
In this paper we are interested in BB knots, namely knots and links where the bridge index equals the braid index. Supported by observations from experiments, it is conjectured tha…