partitions(n [,all:T]) |

Usage: partitions(n), where n > 0 is an integer, computes a matrix with n rows whose columns are the partitions of n (padded with 0). partitions(n,all:T) returns a structure R with n components, such that R[j] is a matrix with j rows whose columns are the partitions of j (padded with 0). NOTE: A partition of an integer N is a set of positive integers {n1,n2,...} such that n1 + n2 + ... = N. Examples: Cmd> partitions(4) # all 5 partitions of 4; rows add to 4 (1,1) 4 0 0 0 (2,1) 3 1 0 0 (3,1) 2 2 0 0 (4,1) 2 1 1 0 (5,1) 1 1 1 1 Cmd> partitions(3,all:T) # partitions of 1, 2 and 3 component: Parts_of_1 (1,1) 1 component: Parts_of_2 (1,1) 2 0 (2,1) 1 1 component: Parts_of_3 (1,1) 3 0 0 (2,1) 2 1 0 (3,1) 1 1 1

Gary Oehlert 2003-01-15