Determinant of links, spanning trees, and a theorem of Shank
2016
In this note, we first give an alternative elementary proof of the relation between the determinant of a link and the spanning trees of the corresponding Tait graph. Then, we use this relation to give an extremely short, knot theoretical proof of a theorem due to Shank stating that a link has component number one if and only if the number of spanning trees of its Tait graph is odd.
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