ALTERNATING SUM FORMULAE FOR THE DETERMINANT AND OTHER LINK INVARIANTS
2010 ◽
Vol 19
(06)
◽
pp. 765-782
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Keyword(s):
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.
2021 ◽
Vol 30
(01)
◽
pp. 2150004
Keyword(s):
Keyword(s):
1998 ◽
Vol 179
(1-3)
◽
pp. 155-166
◽
2016 ◽
Vol 25
(09)
◽
pp. 1641005
2015 ◽
Vol 91
(3)
◽
pp. 353-367
◽
2006 ◽
Vol 15
(10)
◽
pp. 1279-1301