منابع مشابه
Computing Chebyshev knot diagrams
A Chebyshev curve C(a, b, c, φ) has a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + φ), where a, b, c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ R. When C(a, b, c, φ) is nonsingular, it defines a polynomial knot. We determine all possible knot diagrams when φ varies. Let a, b, c be integers, a is odd, (a, b) = 1, we show that one can list all pos...
متن کاملInvariants of Knot Diagrams
We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal number of Reidemeister moves needed to pass between certain pairs of knot diagrams.
متن کاملGenerating Large Random Knot Diagrams
In this paper, we study the problem of generating large random knot diagrams, namely 4-regular planar graphs that are regular projections of prime knots or links. We propose two methods and explore various questions that arise along the way.
متن کاملGraphic lambda calculus and knot diagrams
The graphic lambda calculus [5] is a formalism based on local or global moves acting on locally planar trivalent graphs. In the mentioned paper we showed that ”sectors” of this calculus are equivalent with untyped lambda calculus or with emergent algebras. (The formalism of emergent algebras [2] [3] evolved from differential calculus on metric spaces with dilations [1].) For all the relevant no...
متن کاملUniversal Characteristics of Polygonal Knot Probabilities
There is a striking qualitative similarity among the graphs of the relative probabilities of corresponding knot types across a wide range of random polygon models. In many cases one has theoretical results describing the asymptotic decay of these knot probabilities but, in the finite range, there is little theoretical knowledge and a variety of functional models have been used to fit the observ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2019
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216519500317