Garside combinatorics for Thompson's monoid $F^{+}$ and a hybrid with the braid monoid $B\_{\infty }^{+}$

Patrick Dehornoy, Emilie Tesson

On the model of simple braids, defined to be the left divisors of Garside's elements $\Delta \_n$ in the monoid $B\_{\infty }^{+}$ , we investigate simple elements in Thompson's monoid $F^{+}$…