Definition:Alternating Diagram

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