  We introduce a combinatorial model based on measured foliations in surfaces
which captures the phenomenology of open/closed string interactions. The
predicted equations are derived in this model, and new equations can be
discovered as well. In particular, several new equations together with known
transformations generate the combinatorial version of open/closed duality. On
the topological and chain levels, the algebraic structure discovered is new,
but it specializes to a modular bi-operad on the level of homology.
