Alternating Sum Formulae for the Determinant and Other Link Invariants
نویسنده
چکیده
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 j-th coefficient of the Jones polynomial is given by sub-dessins of genus less or equal to j.
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