Computing permanents and counting Hamiltonian cycles by listing dissimilar vectors
We show that the permanent of an n × n matrix over any finite ring of r ≤ n elements can be computed with a deterministic 2n−Ω(nr ) time algorithm. This improves on a Las Vegas algorithm running in expected 2n−Ω(n/(r log r)) time, implicit in [Björklund, Husfeldt, and Lyckberg, IPL 2017]. For the permanent over the integers of a 0/1-matrix with exactly d ones per row and column, we provide a deter