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First Non-Zero Terms for the Taylor Expansion at 1 of the Conway Potential Function / Buryak A.Yu. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 1. P. 57-59 [Moscow Univ. Math. Bulletin. Vol. 66, No 1, 2011. P. 41-43]. The Conway potential function ∇L(t1,...t1) of an ordered oriented link L=L1∪L2∪...∪Ll⊂S3 is considered. In general, this function is not determined by the linking numbers and the Conway potential functions of the components. However, the first two nonzero terms of the Taylor expansion at the point 1 of the function ∇L are determined by the linking numbers only. We give the explicit formulas for these terms using summation over trees with l vertices.
Key words: link, Conway potential function, Taylor expansion.
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