On some counting problems for semi-linear sets

Flavio D'Alessandro, Benedetto Intrigila, Stefano Varricchio

Let $X$ be a subset of ${\mathbb{N}}^t$ or ${\mathbb{Z}}^t$. We can associate with $X$ a function ${\mathcal{G}}_X:{\mathbb{N}}^t⟶\mathbb{N}$ which returns, for every $(n_1,...,n_t)\in {\mathbb{N}}^t$, the number ${\c…