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- Title
ON TANGLES AND MATROIDS.
- Authors
HUGGETT, STEPHEN
- Abstract
Given matroids M and N there are two operations M ⊕2 N and M ⊗ N. When M and N are the cycle matroids of planar graphs these operations have interesting interpretations on the corresponding link diagrams. In fact, given a planar graph there are two well-established methods of generating an alternating link diagram, and in each case the Tutte polynomial of the graph is related to a polynomial invariant (Jones or Homfly) of the link. Switching from one of these methods to the other corresponds in knot theory to tangle insertion in the link diagrams, and in combinatorics to the tensor product of the cycle matroids of the graphs.
- Subjects
MATROIDS; COMBINATORICS; GRAPH theory; GRAPHIC methods; INVARIANTS (Mathematics); KNOT theory; LOW-dimensional topology
- Publication
Journal of Knot Theory & Its Ramifications, 2005, Vol 14, Issue 7, p919
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216505004147