  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 $F^+$ and in a larger monoid $H^+$ that is a
hybrid of $B\_\infty^+$ and $F^+$ : in both cases, we count how many simple
elements left divide the right lcm of the first n -- 1 atoms, and characterize
their normal forms in terms of forbidden factors. In the case of $H^+$, a
generalized Pascal triangle appears.
