In conversations with Daan Krammer at Warwick, he suggested that the word length metric might be a useful measure. This is not the word length wrt to the Artin generators, but uses either Garside's new or old presentation. (See notes.) Unlike the Artin word length, the shortest length for the Garside presentations (I think for both?) is computationally tractable.
So I suppose we first need the Artin-to-Garside conversion.
In conversations with Daan Krammer at Warwick, he suggested that the word length metric might be a useful measure. This is not the word length wrt to the Artin generators, but uses either Garside's new or old presentation. (See notes.) Unlike the Artin word length, the shortest length for the Garside presentations (I think for both?) is computationally tractable.
So I suppose we first need the Artin-to-Garside conversion.