intPart {kStatistics}

Integer partitions

Description

The function generates all possible (unique) decomposition of a positive integer n in the sum of positive integers less or equal to n.

Usage

intPart(n=0 ,vOutput = FALSE) 

Arguments

n

integer

vOutput

optional boolean parameter, if equal to TRUE the function produces a compact output that is easy to read.

Details

A partition of an integer n is a sequence of weakly increasing integers such that their sum returns n. The intPart function generates all the partitions of a given integer in increasing order.

Value

list

all the partitions of n

Note

Called by the mkmSet function in the kStatistics package.

Author(s)

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

References

A. Nijenhuis, H. Wilf. (1978) Combinatorial Algorithms for Computers and Calculators. Academic Press, Orlando FL, II edition.

See Also

mkmSet, mCoeff, nStirling2, countP, ff

Examples

# Return the partition of the integer 3, that is 
# [1,1,1],[1,2],[3]
intPart(3) 

# Return the partition of the integer 4, that is 
# [1,1,1,1],[1,1,2],[1,3],[2,2],[4]
intPart(4) 
# OR (same output) 
intPart(4, FALSE) 

# Return the same output as the previous example but in a compact expression
intPart(4, TRUE)