3-coloring and other elementary invariants of knots

By Józef H. Przytycki. 2006

119 citations recorded by the source corpus.

Classical knot theory studies the position of a circle (knot) or of several circles (link) in R or S = R3∪∞. The fundamental problem of classical knot theory is the classification of links (including knots) up to the natural movement in space which is called an ambient isotopy. To distinguish knots or links we look for invariants of links, that is, properties of links which are unchanged under ambient isotopy. When we look for invariants of links we have to take into account the following three criteria:

Subfields: Genetics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06a555c9550a19d3528810cf819ee62d06892452

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In Genetics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Problems on invariants of knots and 3-manifolds (2004, background): “Przytycki [337] studied the number of 3-colorings.”
Knot invariants derived from quandles and racks (2002, background): “Fox’s 3-colorings are representations of the knot quandle to the dihedral kei of order 3 and generalized Fox’s colorings (n-colorings) are representations to the dihedral kei of order n [11, 16, 25].”