RANDOM K-SET OF N-SET

RANDOM K-SET OF N-SET (LET)

Let Subcommand

Generate a random k-set of a an n-set.

Given a set of n elements {1, 2, ..., n}, a basic combinatorial problem is the combination of n things taken k at a time. For a given n and k, there are

k-sets of the original n-set.

This command generates a single random k-set.

The output is an array of size k that identifies the elements included in the k-set.

LET <y> = RANDOM K-SET OF N-SET             FOR I = 1 1 <k>
where <k> is a number or parameter that specifies the size of the k-set;
and     <y> is a variable where the random k-set is saved.

This command must be preceeded with the command

LET N = <value>

LET N = 5
LET K = 3
LET Y = RANDOM K-SET OF N-SET FOR I = 1 1 K

Dataplot implements this command using the RANKSB 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 COMPOSITION	= Generate a random composition.
RANDOM PARTITION	= Generate a random partition.
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 4.

Combinatorial Analysis

2008/4

 
LET N = 8
LET K = 3
LET Y = RANDOM K-SET OF N-SET FOR I =  1  1  K
PRINT Y