ConsRank (version 2.1.5)

univranks: Generate the universe of rankings

Description

Generate the universe of rankings given the input partition

Usage

univranks(X, k = NULL, ordering = TRUE)

Value

a "list" containing the following components:

Runiv		The universe of rankings
Cuniv		A list containing:
	R	The universe of rankings in terms of rankings;
	Parts	for each ranking in input the produced rankings
	Univinbuckets	the universe of rankings within each bucket

Arguments

X

A ranking, an ordering, a matrix of rankings, a matrix of orderings or a number

k

Optional: the number of the non-empty subsets. It has to be used only if X is anumber. The default value is NULL, In this case the universe of rankings with n=X items are computed

ordering

The universe of rankings must be returned as orderings (default) or rankings?

Author

Antonio D'Ambrosio

Details

The function should be used with small numbers because it can generate a large number of permutations. The use of X greater than 9, of X matrices with more than 9 columns as input is not reccomended.

See Also

stirling2 Stirling number of second kind.

rank2order Convert rankings into orderings.

order2rank Convert orderings into ranks.

partitions Generate partitions of n items constrained into k non empty subsets.

Examples

S2<-stirling2(4,4)$SM[4,] #indicates in how many ways 4 objects
                         #can be placed, respectively, into 1, 2,
                         #3 or 4 non-empty subsets.
CardConstr<-factorial(c(1,2,3,4))*S2  #the cardinality of rankings 
                                     #constrained into 1, 2, 3 and 4
                                     #buckets
Card<-sum(CardConstr)  #Cardinality of the universe of rankings with 4
                      #objects                                                              
U<-univranks(4)$Runiv #the universe of rankings with four objects
                     # we know that the universe counts 75 
                     #different rankings
Uk<-univranks(4,2)$Runiv    #the universe of rankings of four objects 
                           #constrained into k=2 buckets, we know they are 14
Up<-univranks(c(1,4,3,1))$Runiv  #the universe of rankings with 4 objects
                                #for which the first and the fourth item
                                #are tied