Douglas da Silva Ferreira Brilhante

Fixed-excess simple paths in multidimensional king graphs

Let K_{d,n} = P_n^{⊠d} be the d-fold strong product of a path, with opposite corners s and t. For k ≥ 0, let C_{d,k}(n) count simple s–t paths with n − 1 + k edges. Coordinate deficits show that every such path has at most dk moves other than the positive main diagonal. We prove...