Definition:Alternating Diagram
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Definition
Let $K$ be a knot whose planar representation is $P$.
$K$ has an alternating diagram if and only if $P$ is such that the string of $P$ crosses over and under alternately.
Also see
- Results about alternating diagrams can be found here.
Historical Note
Knots with alternating diagrams were originally studied by Peter Guthrie Tait.
He conjectured that such a knot cannot be reduced to the unknot.
This was subsequently proved by using the Jones polynomial.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): knot theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): knot theory