Add to ORKGAbstract. This paper determines the minimal degree sequence for two com-pact rational knots, namely the trefoil and figure-eight knots. We find explicit projections with the minimal degree sequence of each knot. This is done by modifying a non-compact rational minimal-degree parameterization of the tre-foil and figure-eight knots to make it compact. This research was conducted at Ramapo College of New Jersey during the summer of 2011 with Dr. Donova
AbstractWe describe the explicit form and the hidden structure of the answer for the HOMFLY polynomi...
Abstract. By the works of Kondo and Sakai, it is known that Alexander polynomi-als of knots which ar...
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...
Polynomial knots were introduced by Vasiliev and are now studied by many mathematicians. They are im...
The structure of classical minimal prime knot presentations suggests that there are often, perhaps a...
Looking at the structure of minimal prime knot presentations, one can notice that there are often, p...
We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better unde...
AbstractIn a paper by G. Buck and J. Simon a potential energy function for piecewise linear knots is...
Differential expansion (DE) for a Wilson loop average in representation R is built to respect degene...
AbstractDifferential expansion (DE) for a Wilson loop average in representation R is built to respec...
AbstractA Chebyshev knot C(a,b,c,φ) is a knot which has a parametrization of the form x(t)=Ta(t);y(t...
International audienceWe study the degree of polynomial representations of knots. We give the lexico...
example of a knot where the unknotting number was not realized in a minimal projection of the knot. ...
This article concerns the minimal knotting number for several types of lattices, including the face-...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
AbstractWe describe the explicit form and the hidden structure of the answer for the HOMFLY polynomi...
Abstract. By the works of Kondo and Sakai, it is known that Alexander polynomi-als of knots which ar...
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...
Polynomial knots were introduced by Vasiliev and are now studied by many mathematicians. They are im...
The structure of classical minimal prime knot presentations suggests that there are often, perhaps a...
Looking at the structure of minimal prime knot presentations, one can notice that there are often, p...
We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better unde...
AbstractIn a paper by G. Buck and J. Simon a potential energy function for piecewise linear knots is...
Differential expansion (DE) for a Wilson loop average in representation R is built to respect degene...
AbstractDifferential expansion (DE) for a Wilson loop average in representation R is built to respec...
AbstractA Chebyshev knot C(a,b,c,φ) is a knot which has a parametrization of the form x(t)=Ta(t);y(t...
International audienceWe study the degree of polynomial representations of knots. We give the lexico...
example of a knot where the unknotting number was not realized in a minimal projection of the knot. ...
This article concerns the minimal knotting number for several types of lattices, including the face-...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
AbstractWe describe the explicit form and the hidden structure of the answer for the HOMFLY polynomi...
Abstract. By the works of Kondo and Sakai, it is known that Alexander polynomi-als of knots which ar...
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...