We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that of Mezard et al. (2005) to rigorously prove that for some values of the order parameter the overlap distribution of k-Exact Cover has discontinuous support.

翻译：我们证明了 q-重叠-k-精确覆盖问题阈值的上下界。这些结果受到统计物理中一步复制对称破缺方法的启发，并希望基于 Mezard 等人（2005）的方法，严格证明对于某些序参数值，k-精确覆盖的重叠分布具有不连续支撑集。