An Arithmetic Triangle Arising From a One-Way Street Grid. (15th March 2023) - Richmond, Tom; Sword, Mia
Summary: Pascal's triangle arises by counting the number of shortest paths from (0, 0) to ( n, k ) on a square street grid. The length of the shortest path is the Manhattan distance from (0, 0) to ( n, k ). We consider the case of a square street grid of one-way streets, with successive parallel streets being oppositely directed. We investigate the associated distance function q (which is only a quasi-metric, since q ( A, B ) may differ from q ( B, A )) and the arithmetic triangle obtained by counting shortest routes on the one-way grid from (0, 0) to ( n, k ).