The purpose of this note is to answer Question 6.12 of Etnyre and Van Horn-Morris [Monoids in the mapping class group, Geom. Topol. Monographs 19 (2015) 319–365], asking when the set of mapping classes whose fractional Dehn twist coefficient is greater than a given constant forms a monoid.
"On a question of Etnyre and Van Horn-Morris." Algebr. Geom. Topol. 17 (1) 561 - 566, 2017. https://doi.org/10.2140/agt.2017.17.561