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partitions()

Usage:
partitions(n [,all:T])



Keywords: integers
                                  Usage
partitions(n), where n > 0 is an integer, computes a matrix with n
columns whose rows, possibly padded with 0, are the partitions of n.  A
partition of n is a non-increasing set of integers summing to n.

partitions(n,all:T) returns a structure R with n components, such that
R[j] is a matrix with j columns whose rows are the partitions of j
(padded with 0).

The number N of partitions of n grows fairly rapidly:
  n     N     n     N     n     N     n     N
  1     1     7    15    13   101    19   490
  2     2     8    22    14   135    20   627
  3     3     9    30    15   176    21   792
  4     5    10    42    16   231    22  1002
  5     7    11    56    17   297    23  1255
  6    11    12    77    18   385    24  1575

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 2006-01-30