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Converted {{Multiple issues}} to new format to fix expert parameter & general fixes using AWB (8853) |
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An important example of a length is the [[word metric]]: given a [[presentation of a group]] by generators and relations, the length of an element is the length of the shortest word expressing it.
[[Coxeter group]]s (including the [[symmetric group]]) have combinatorial important length functions, using the simple reflections as generators (thus each simple reflection has length 1). See also: [[length function of a Weyl group element]].
A [[longest element of a Coxeter group]] is both important and unique up to conjugation (up to different choice of simple reflections).
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