35 citations · 57 across the 24 of their papers we have counts for
17 papers · 1 filter
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…
The Ropelength of Special Alternating Knots
Yuanan Diao
A long standing open conjecture states that if a link is alternating, then its ropelength is at least of the order . A recent res…
Writhe-like invariants of alternating links
Yuanan Diao, Van Pham
It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict o…
The number of oriented rational links with a given deficiency number
Yuanan Diao, Michael Finney, Dawn Ray
Let be the set of un-oriented and rational links with crossing number , a precise formula for was obtained by Ernst and Sumners in 1987. In this paper, we study th…
Braid Index Bounds Ropelength From Below
Yuanan Diao
For an un-oriented link , let be the ropelength of . It is known that when has more than one component, different orientati…
A Diagrammatic Approach for Determining the Braid Index of Alternating Links
Yuanan Diao, Claus Ernst, Gabor Hetyei +1
It is well known that the braid index of a link equals the minimum number of Seifert circles among all link diagrams representing it. For a link with a reduced alternating diagram…
The Braid Index Of Reduced Alternating Links
Yuanan Diao, Gábor Hetyei, Pengyu Liu
It is well known that the minimum crossing number of an alternating link equals the number of crossings in any reduced alternating link diagram of the link. This remarkable result…
The HOMFLY Polynomial of Links in Closed Braid Form
Pengyu Liu, Yuanan Diao, Gábor Hetyei
It is well known that any link can be represented by the closure of a braid. The minimum number of strings needed in a braid whose closure represents a given link is called the bra…
Nullification of knots and links
Yuanan Diao, Claus Ernst, Anthony Montemayor
In this paper, we study a geometric/topological measure of knots and links called the nullification number. The nullification of knots/links is believed to be biologically relevant…
The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers
Yuanan Diao, Claus Ernst, Attila Por +1
For a knot or link K, let L(K) be the ropelength of K and Cr(K) be the crossing number of K. In this paper, we show that there exists a constant a>0 such that L(K) is bounded above…
Tutte Polynomials of Tensor Products of Signed Graphs and their Applications in Knot Theory
Y. Diao, G. Hetyei, K. Hinson
It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Rely…
Quadrisecants give new lower bounds for the ropelength of a knot
Elizabeth Denne, Yuanan Diao, John M Sullivan
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical…