Skein

A skein is a length of yarn or thread wound into a loose, elongated coil, often used in hand knitting and weaving. It is typically a strand of yarn wound into a tangle-free loop that allows the filament to be drawn from the outside as it is worked. Skeins differ in shape from balls or hanks: a ball is wound into a solid sphere, a hank is a looped coil that must be unwound before use. In commerce, skeins are commonly sold by weight or length, and instructions may specify the yardage per skein. After use, a skein may be wound into a ball or cake to prevent tangling.

A skein also refers to a group of flying geese or swans. In ornithology and literature, a skein describes the V-shaped or clustered flight formation of geese or other waterfowl, typically observed at migration.

In knot theory, skein denotes a relation among knot diagrams that differ only at a single crossing. Skein relations are used to define and compute knot invariants, such as the Alexander and HOMFLY-PT polynomials, by relating simpler diagrams to more complex ones. A skein setup usually involves three links L+, L-, and L0 that differ locally at a crossing.