Geodesic
A~formula for the generalized Sato--Levine invariant
Sbornik. Mathematics, Tome 192 (2001) no. 1, pp. 1-10

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Let $W$ be the generalized Sato–Levine invariant, that is, the unique Vassiliev invariant of order 3 for two-component links that is equal to zero on double torus links of type $(1,k)$. It is proved that $$ W=\beta-\frac{k^3-k}6\,, $$ where $\beta$ is the invariant of order 3 proposed by Viro and Polyak in the form of representations of Gauss diagrams and $k$ is the linking number. 
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     title = {A~formula for the generalized {Sato--Levine} invariant},
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P. M. Akhmet'ev; I. Maleshich; D. Repovš. A~formula for the generalized Sato--Levine invariant. Sbornik. Mathematics, Tome 192 (2001) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/SM_2001_192_1_a0/