Displaying similar documents to “3-coloring and other elementary invariants of knots”

Generalized n-colorings of links

Daniel Silver, Susan Williams (1998)

Banach Center Publications

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The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced by R. H. Fox. For any positive integer n the various (n,r)-colorings of a diagram for an oriented link l correspond in a natural way to the periodic points of the representation shift Φ / n ( l ) of the link. The number of (n,r)-colorings of a diagram for a satellite knot is determined by the colorings of its pattern and companion knots together with the winding number.

Arc presentations of knots and links

Peter Cromwell (1998)

Banach Center Publications

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s paper presents some examples and a survey of results concerning a new way of presenting knots and links, together with the corresponding link invariant. More detailed accounts are given in [Cr, C-N, Nu1, Nu2, Nu3].

Adequacy of Link Families

Slavik Jablan, Ljiljana Radović, Radmila Sazdanović (2010)

Publications de l'Institut Mathématique

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Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics

Józef Przytycki (1995)

Banach Center Publications

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We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones, transplants into knot theory the idea of the Yang-Baxter equation with the spectral parameter (idea employed by Baxter in the theory of solvable models in statistical...

Twisting and unknotting operations.

Yoshiyuki Ohyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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We define a twisting move, an (n,k)-move, on a link diagram and consider the question as to whether or not any two links are equivalent by this move. Moreover we show that any knot can be trivialized by at most twice twisting operations.

Positive knots, closed braids and the Jones polynomial

Alexander Stoimenow (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Using the recent Gauß diagram formulas for Vassiliev invariants of Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality, we prove several inequalities for positive knots relating their Vassiliev invariants, genus and degrees of the Jones polynomial. As a consequence, we prove that for any of the polynomials of Alexander/Conway, Jones, HOMFLY, Brandt-Lickorish-Millett-Ho and Kauffman there are only finitely many positive knots with the same polynomial and no...

Invariants of piecewise-linear knots

Richard Randell (1998)

Banach Center Publications

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We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.