... ,thenanypoint zjlies inside the triangle determined by the preceding three points in thisordering.To start the induction, for k =1wechoosez1to be a point, for k =2letz1andz2be any two distinct ... the distri-bution of longest increasing subsequences in random permutations, in preparation.[11] A. M. Odlyzko and E. M. Rains, On longest increasing subsequences in random permutations, to be ... (3.2)The ordering of the projections of the xjis obtained from the same diamond westarted with, but after interchanging the t + 1 extreme pairs of points in the initialordering. For example,...