 The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie.In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end.Thus enumerating tie knots of "n" moves is equivalent to enumerating walks of "n" steps.