PositivePermutationBraid

The unique positive braid realising a permutation in which no pair of strands crosses more than once.

PositivePermutationBraid(permutation)the positive braid with no pair crossing twice

Typed signatures

Type	Package	Applies
(list<integer>) -> expression<Braid>	braid	always

Domain: Braids and knots

Examples

Basic #

$\sigma_1\sigma_2\sigma_1$, the half twist

live ↗

In$\mathrm{PositivePermutationBraid}(\bigl\lbrack3, 2, 1\bigr\rbrack)$Out$\mathrm{Braid}(3, \bigl\lbrack1, 2, 1\bigr\rbrack)$

Each pair crosses at most once

live ↗

In$\mathrm{PositivePermutationBraid}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$\mathrm{Braid}(3, \bigl\lbrack2, 1\bigr\rbrack)$

About

Examples	2

See also: BraidPermutation, LorenzBraid