Permuting

Cable patterns are made by permuting the order of stitches; although one or two stitches may be held by hand or knit out of order, cables of three or more generally require a cable needle.

Conjugation (parastrophe) Left and right division are examples of forming a quasigroup by permuting the variables in the defining equation.

For example, S 3 acts faithfully and transitively on a set with exactly three elements (by permuting them).

For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C. Any Latin square can be reduced by permuting (that is, reordering) the rows and columns.

In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too).

It is similar to the layer-by-layer method but employs the use of a large number of algorithms, especially for orienting and permuting the last layer.

This is then followed by orienting the last layer, then permuting the last layer (OLL and PLL respectively).