3 research outputs found
q-Overlaps in the Random Exact Cover Problem
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.Comment: In Proceedings FROM 2023, arXiv:2309.1295