On a generalization of the seating couples problem

Abstract

We prove a conjecture of Adamaszek generalizing the seating couples problem to the case of $2n$ seats. Concretely, we prove that given a positive integer $n$ and $d_1,\dots ,d_n\in (\mathbb{Z}/2n{)}^{\ast }$ we can partition $\mathbb{Z}/2n$ into $n$ pairs with differences $d_1,\dots ,d_n$.

3 pages