Dataplot Vol 2 Vol 1

# RANDOM PARTITION

Name:
RANDOM PARTITION (LET)
Type:
Let Subcommand
Purpose:
Generate a random partition of a positive integer.
Description:
Given a positive integer n, a partition of n is defined as

n = r1 + r2 + ... + rk             (r1r2 ≥ ... ≥ rk)

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

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

 6 = 4 + 1 + 1 = 3 + 2 + 1 = 2 + 2 + 2
Syntax:
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>
Examples:
LET N = 5
LET Y = RANDOM PARTITION
Note:
Dataplot implements this command using the RANPAR algorithm described in Nijenhuis and Wilf (see Reference section below).
Note:
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.

Default:
None
Synonyms:
None
Related Commands:
 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.
Reference:
Nijenhuis and Wilf (1978), "Combinatorial Algorithms", Second Edition, Academic Press, Chapter 10.
Applications:
Combinatorial Analysis
Implementation Date:
2008/4
Program:
```
LET N = 8
LET Y = RANDOM PARTITION
PRINT Y
```

Date created: 1/12/2009
Last updated: 1/12/2009