Title

Alternating sum formulae for the determinant and other link invariants

Document Type

Article

Publication Date

6-1-2010

Abstract

A classical result states that the determinant of an alternating link is equal to the number of spanning trees in a checkerboard graph of an alternating connected projection of the link. We generalize this result to show that the determinant is the alternating sum of the number of quasi-trees of genus j of the dessin of a non-alternating link. Furthermore, we obtain formulas for coefficients of the Jones polynomial by counting quantities on dessins. In particular, we will show that the jth coefficient of the Jones polynomial is given by sub-dessins of genus less or equal to j. © 2010 World Scientific Publishing Company.

Publication Source (Journal or Book title)

Journal of Knot Theory and its Ramifications

First Page

765

Last Page

782

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