# Generalized n-colorings of links

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 381-394
- ISSN: 0137-6934

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topSilver, Daniel, and Williams, Susan. "Generalized n-colorings of links." Banach Center Publications 42.1 (1998): 381-394. <http://eudml.org/doc/208818>.

@article{Silver1998,

abstract = {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.},

author = {Silver, Daniel, Williams, Susan},

journal = {Banach Center Publications},

keywords = {-coloring; satellite knot},

language = {eng},

number = {1},

pages = {381-394},

title = {Generalized n-colorings of links},

url = {http://eudml.org/doc/208818},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Silver, Daniel

AU - Williams, Susan

TI - Generalized n-colorings of links

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 381

EP - 394

AB - 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.

LA - eng

KW - -coloring; satellite knot

UR - http://eudml.org/doc/208818

ER -

## References

top- [BuZi] G. Burde and H. Zieschang, Knots, de Gruyter Stud. in Math. 5, de Gruyter, Berlin, 1985.
- [CrFo] R. H. Crowell and R. H. Fox, An Introduction to Knot Theory, Ginn and Co., 1963. Zbl0126.39105
- [Fo1] R. H. Fox, A quick trip through knot theory, in: Topology of 3-Manifolds and Related Topics, M. K. Fort (ed.), Prentice-Hall, N.J. (1961), 120-167.
- [Fo2] R. H. Fox, Metacyclic invariants of knots and links, Canad. J. Math. 22 (1970), 193-201. Zbl0195.54002
- [Ha] R. Hartley, Metabelian representations of knot groups, Pacific J. Math. 82 (1979), 93-104. Zbl0404.20032
- [HaKe] J. C. Hausmann and M. Kervaire, Sous-groupes dérivés des groupes de noeuds, L'Enseign. Math. 24 (1978), 111-123. Zbl0414.57012
- [Lt] R. A. Litherland, Cobordism of satellite knots, Contemp. Math. 35 (1984), 327-362.
- [LvMe] C. Livingston and P. Melvin, Abelian invariants of satellite knots, in: Geometry and Topology, C. McA. Gordon (ed.), Lecture Notes in Math. 1167, Springer, Berlin, 1985, 217-227.
- [LySc] R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin, 1977.
- [Pr] J. H. Przytycki, 3-coloring and other elementary invariants of knots, these proceedings.
- [Re] K. Reidemeister, Knotentheorie, Ergeb. Math. Grenzgeb. 1, Springer, Berlin, 1932; English translation: Knot Theory, BCS Associates, Moscow, Idaho, 1983.
- [Ro] D. Rolfsen, Knots and Links, Math. Lecture Ser. 7, Publish or Perish Inc., Berkeley, 1976. Zbl0339.55004
- [Sc] H. Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 131-286.
- [Se] H. Seifert, On the homology invariants of knots, Quart. J. Math. Oxford 2 (1950), 23-32. Zbl0035.11103
- [SiWi1] D. S. Silver and S. G. Williams, Augmented group systems and shifts of finite type, Israel J. Math. 95 (1996), 231-251. Zbl0899.20011
- [SiWi2] D. S. Silver and S. G. Williams, Knot invariants from symbolic dynamical systems, Trans. Amer. Math. Soc., to appear.

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