AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of its prime components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial improvement on previous results. The proof depends essentially on writing links in terms of their arc-presentations, and has as a key ingredient Bae and Park's theorem that an n-crossing link has an arc-presentation with less than or equal to n+2 arcs
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit d...
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
AbstractFor a link K, let L(K) denote the ropelength of K and let Cr(K) denote the crossing number o...
A model of the pretzel knot is described. A method for predicting the ropelength of pretzel knots ...
AbstractFor a knot or link K, L(K) denotes the rope length of K and Cr(K) denotes the crossing numbe...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
Abstract. The ropelength of a knot is the quotient of its length by its thick-ness, the radius of th...
The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest e...
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is...
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered...
An n-crossing is a point in the projection of a knot where n strands cross so that each strand bisec...
For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more...
For a certain infinite family of knots or links, we study the growth power ratios of their stick num...
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit d...
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
AbstractFor a link K, let L(K) denote the ropelength of K and let Cr(K) denote the crossing number o...
A model of the pretzel knot is described. A method for predicting the ropelength of pretzel knots ...
AbstractFor a knot or link K, L(K) denotes the rope length of K and Cr(K) denotes the crossing numbe...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
Abstract. The ropelength of a knot is the quotient of its length by its thick-ness, the radius of th...
The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest e...
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is...
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered...
An n-crossing is a point in the projection of a knot where n strands cross so that each strand bisec...
For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more...
For a certain infinite family of knots or links, we study the growth power ratios of their stick num...
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit d...
The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general...