> group theorists would normally draw permutations as collection of directed
> cycles, with labelled vertices.

I would somewhat also expect this to be the default drawing of a
permutation. Especially, when a permutation has a lot of fix points,
diagram presentations get kind of messy. Imagine the permutation
(1,2)(23,24) in S_n for some big n. What about an optional argument
for various drawing methods that can be something like

- "cycle" (my favorite for the default)
- "braid" (this is the one you were proposing, Nathaan - very nice
also when one can also get such a braid for multiple permutations
concatenated)
- "one-line" (which puts all letters 1..n on a line and then draw
directed arcs to the right on top and to the left on bottom; very
usefull when studying noncrossing or nonnesting permutations)
- "chord-diagram" (all points on a circle and then oriented edges
within the circle)

Just my 2 cents, Christian

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