Designing tie knots by random walks

Abstract

The simplest of conventional tie knots, the four-in-hand, has its origins in late-nineteenth-century England. The Duke of Windsor, as King Edward VIII became after abdicating in 1936, is credited with introducing what is now known as the Windsor knot, from which its smaller derivative, the half-Windsor, evolved. In 1989, the Pratt knot, the first new knot to appear in fifty years, was revealed on the front page of The New York Times.