A skein relation relates the invariants of link diagrams agreeing outside a disk and differing by a positive crossing, a negative crossing, and a smoothing within it. Its signs and normalization determine the particular invariant convention.
The oriented smoothing replaces a crossing by two disjoint arcs whose orientations agree with the four oriented ends. It is the zero-resolution in an oriented skein relation.
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"Skein relation" refers to a concept in the study of knots and links within the field of topology, specifically in knot theory. Skein relations are equations that express the relationships between different knots or links under certain conditions. These relations are often used in the computation of polynomial invariants of knots and links, such as the Jones polynomial or the HOMFLY-PT polynomial. The basic idea behind skein relations is to define a knot or link in terms of simpler components.