m2Set {kStatistics}

Detecting equal columns in multi-index partitions

Description

The function returns the vectors (only counted once) of all the multi-index partitions output of the mkmSet function. These vectors correspond also to the blocks of the subdivisions of the multiset having the given multi-index as multeplicites.

Usage

m2Set( v=c(0) ) 

Arguments

v

sequence of type [[e1,e2,...], m1], [[f1,f2,...], m2],... with m1, m2,... multiplicities

Details

Consider the multi-index (2,1). The partitions are
⁠ 0 1 1 0 2 1 1 2 1 0 0 1 0 0 1 1⁠

with multiplicities 1, 1, 2, 1 respectively. The m2Set function deletes column repetitions, that is transforms the given list in [[0,1],[1,0],[2,0],[1,1],[2,1]] according to the order given in the input. In terms of subdivisions, suppose to consider the multiset [a,a,b] with multiplicities (2,1). The subdivisions are

[[[b],[a],[a]],1], [[[a,a],[b]],1], [[[a],[a,b]],2], [[a,a,b],1].

The m2Set function deletes block repetitions, that is transforms the given list in

[[b],[a],[a,a],[a,b],[a,a,b]]

according to the order given in the input. See also the examples.

Value

set

the sequence with distinct elements

Note

Called by the nKM and nPM functions in the kStatistics package.

Author(s)

Elvira Di Nardo [e-mail],
Giuseppe Guarino [e-mail]

See Also

list2m, list2Set

Examples

M1 <- mkmSet(c(2,1))
# M1 is  
#  list(   
#       list( list(  c(0,1), c(1,0), c(1,0) )  ,1),
#       list( list(  c(0,1), c(2,0)         )  ,1), 
#       list( list(  c(1,0), c(1,1)         )  ,2),            
#       list( list(  c(2,1)                 )  ,1),    
#      )
# To print all the partitions of the multi-index (2,1) run mkmSet(c(2,1),TRUE)
#   [( 0 1 )( 1 0 )( 1 0 ),  1 ]
#   [( 0 1 )( 2 0 ),  1 ]
#   [( 1 0 )( 1 1 ),  2 ] 
#   [( 2 1 ),  1 ]
#
# Then m2Set(M1) returns the following set:  [[0,1],[1,0],[2,0],[1,1],[2,1]]
# 
m2Set( M1 )