Enumerations relating braid and commutation classes
We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these bounds, and enumerate both cases.
European Journal of Combinatorics
Fishel, S., Milicevic, E., Patrias, R., & Tenner, B.E. (2018). Enumerations relating braid and commutation classes. European Journal of Combinatorics 74: 11-26. https://doi.org/10.1016/j.ejc.2018.07.002.