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Tangles

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SNARLS.

Last seen on: Eugene Sheffer – King Feature Syndicate Crossword – Oct 26 2022

Random information on the term “Tangles”:

In mathematics, a tangle is generally one of two related concepts:

(A quite different use of ‘tangle’ appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, Journal of Combinatorial Theory B 52 (1991) 153–190, who used it to describe separation in graphs. This usage has been extended to matroids.)

The balance of this article discusses Conway’s sense of tangles; for the link theory sense, see that article.

Two n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considered analogous to knot theory except instead of closed loops we use strings whose ends are nailed down. See also braid theory.

Without loss of generality, consider the marked points on the 3-ball boundary to lie on a great circle. The tangle can be arranged to be in general position with respect to the projection onto the flat disc bounded by the great circle. The projection then gives us a tangle diagram, where we make note of over and undercrossings as with knot diagrams.

Tangles on Wikipedia

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