# Designing tie knots by random walks

T. Fink, Y. Mao

*Nature* 398, 31 (209)

#tieknots#randomwalks#combinatorics

The number of ways to tie a tie can be enumerated by counting the number of persistent random walks on a triangular lattice.

We developed a mathematical model of tie knots, and provide a map between tie knots and persistent random walks on a triangular lattice. We classify knots according to their size and shape, and quantify the number of knots in each class. The optimal knot in a class is selected by the proposed aesthetic conditions of symme- try and balance. Of the 85 knots that can be tied with a conventional tie, we recover the four knots that are in widespread use and introduce six new aesthetically pleasing knots.

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