Hilbert functions over the exterior algebra and f-vectors in higher rank II: Generalizing Linusson's count to sumsets of f-vectors

Let $E$ be the exterior algebra of an $n$-dimensional vector space over a field, let $F$ be a graded free $E$-module with $r$ generators of degrees $d_1 \le \dots \le d_r$, and let $M$ range over the monomial submodules of Amata and Crupi. The Hilbert function of $F/M$ is a shifted sum of $f$-vector