A non-crossing partition of size n is a partitioning of the set {0,...,n-1} into a finite number of non-empty disjoint pieces such that if a < b belong to one part, and c < d belong to a different part, then a < b < c < d, a < c < d < b, or c < d < a < b.
i1 : ncPartitions 5 o1 = {01234, 0/1234, 0234/1, 0134/2, 0124/3, 0123/4, 01/234, 034/12, 014/23, 012/34, 04/123, 0/1/234, 0/134/2, 0/124/3, 0/123/4, ---------------------------------------------------------------------------------------------------------------------------- 0/12/34, 0/14/23, 034/1/2, 024/1/3, 023/1/4, 02/1/34, 04/1/23, 014/2/3, 013/2/4, 01/2/34, 04/13/2, 012/3/4, 01/24/3, ---------------------------------------------------------------------------------------------------------------------------- 04/12/3, 01/23/4, 03/12/4, 0/1/2/34, 0/1/24/3, 0/1/23/4, 0/14/2/3, 0/13/2/4, 0/12/3/4, 04/1/2/3, 03/1/2/4, 02/1/3/4, ---------------------------------------------------------------------------------------------------------------------------- 01/2/3/4, 0/1/2/3/4} o1 : List |