RANDOM PARTITION

RANDOM PARTITION (LET)

Let Subcommand

Generate a random partition of a positive integer.

Given a positive integer n, a partition of n is defined as
n = r₁ + r₂ + ... + r_k             (r₁ ≥ r₂ ≥ ... ≥ r_k)

where r₁, r₂, ...., r_k are positive integers.

For example, if n = 6, then there are 3 partitions:

6	=	4 + 1 + 1
	=	3 + 2 + 1
	=	2 + 2 + 2

LET <y> = RANDOM PARTITION
where <y> is a variable where the random partition is saved.

This command must be preceeded with the command

LET N = <value>

LET N = 5
LET Y = RANDOM PARTITION

Dataplot implements this command using the RANPAR algorithm described in Nijenhuis and Wilf (see Reference section below).

Dataplot supports a number of different random number generators. Enter HELP RANDOM NUMBER GENERATOR for details.

The SEED command can be used to specify a seed for the random number generator.

None

None

LET	= Generate data transformations.
RANDOM PERMUTATION	= Generate a random permutation.
RANDOM K-SET OF N-SET	= Generate a random k-set of n-set.
RANDOM COMPOSITION	= Generate a random composition.
RANDOM SUBSET	= Generate a random subset.
RANDOM EQUIVALENCE RELATION	= Generate a random equivalence relation.
NEXT SUBSET	= Generate the next subset of a set.
NEXT PERMUTATION	= Generate the next permutation.
NEXT K-SET OF N-SET	= Generate the next k-set of n-set.
NEXT COMPOSITION	= Generate the next composition.
NEXT PARTITION	= Generate the next partition.
NEXT EQUIVALENCE RELATION	= Generate the next composition.

Nijenhuis and Wilf (1978), "Combinatorial Algorithms", Second Edition, Academic Press, Chapter 10.

Combinatorial Analysis

2008/4

 
LET N = 8
LET Y = RANDOM PARTITION
PRINT Y