mpCart {kStatistics}

Join two lists

Description

Given two lists with elements of the same type, the function returns a new list whose elements are the joining of the two original lists, except for the last elements, which are multiplied.

Usage

mpCart( M1 = NULL, M2 = NULL ) 

Arguments

M1

list of vectors

M2

list of vectors

Details

The input of the mpCart function are two lists. Each list might contain multiple lists of two vectors: the first vector contains multisets whose elements are of the same type (integers or vectors with the same lenght), the second vector is a number (for example a multiplicity if the multiset is a subdivision). The mpCart function generates a new list of two vectors: the first is obtained by joining the first vectors in the two input lists, the second is just the product of the numbers in the second vectors. See the examples.

Value

list

the list with the joined input lists

Note

Called by the function nPM in the package kStatistics.

Author(s)

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

References

E. Di Nardo, G. Guarino, D. Senato (2008) An unifying framework for k-statistics, polykays and their generalizations. Bernoulli. 14(2), 440-468. (download from https://arxiv.org/pdf/math/0607623.pdf)

E. Di Nardo, G. Guarino, D. Senato (2008) Symbolic computation of moments of sampling distributions. Comp. Stat. Data Analysis. 52(11), 4909-4922. (download from https://arxiv.org/abs/0806.0129)

E. Di Nardo, G. Guarino, D. Senato (2009) A new method for fast computing unbiased estimators of cumulants. Statistics and Computing, 19, 155-165. (download from https://arxiv.org/abs/0807.5008)

See Also

pCart

Examples

A <- list(  list( list(c(1),c(2) ),c(-1)), list(list(c(3)),c(1))  )
# where 
# -1 is the multiplicative factor of list(c(1),c(2) ) 
#  1 is the multiplicative factor of list(c(3))
B <- list( list( list(c(5)),c(7)))
# where 7 is the multiplicative factor of list(c(5))
 
# Return [[[1],[2],[5]], -7] , [[[3],[5]], 7]
mpCart(A,B) 

A <- list( list( list( c(1,0),c(1,0) ), c(-1)),  list( list( c(2,0)), c(1) ))
# where
# - 1 is the multiplicative factor of list( c(1,0),c(1,0) )
#   1 is the multiplicative factor of list( c(2,0) )
B <- list( list( list( c(1,0)), c(1)) )
# where 1 is the multiplicative factor of list( c(1,0))

# Return [[[1,0],[1,0],[1,0]], -1], [[[2,0],[1,0]],1]
mpCart(A,B)