Number of partitions of modular integers (with an Appendix by P. Deligne)

David Broadhurst, Xavier Roulleau

For integers $n,k,s$, we give a formula for the number $T(n,k,s)$ of order $k$ subsets of the ring $\mathbb{Z}/n\mathbb{Z}$ whose sum of elements is $s$ modulo $n$. To do so, we de…