univranks {ConsRank} R Documentation

## Generate the universe of rankings

### Description

Generate the universe of rankings given the input partition

### Usage

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


### 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?

### 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.

### 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

### Author(s)

Antonio D'Ambrosio antdambr@unina.it

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



[Package ConsRank version 2.1.3 Index]