Last update: 15 March 2013
The lexicographic order on words is given by
A word is Lyndon if it is smaller than all its proper right factors.
Any word has a unique factorisation
(see [Lo, Thm 5.1.5] or [Re, Thm 4.9]).
the words in the set
(displayed in their nonincreasing Lyndon factorisation) are
A word is good if there is a homogeneous element
such that is the maximal word appearing in
. The following proposition gives a characterisation
of good words and good Lyndon words.
[Le, Prop 17, Prop 25] and [LR, Cor 2.5]
- A word is good if and only if
Let be the set of positive roots and let
be the set of good Lyndon words.
Then the map
Notes and References
This page is partially based on joint work with P. Lalonde and A. Kleshchev.