Contents

partitions()

Usage:

partitions(n [,all:T])

Keywords: integers

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