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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/genComp.R
\name{genComp}
\alias{genComp}
\title{Generate all, or a subset, of the integer partitions of an integer n.}
\usage{
genComp(n, len = TRUE, addZeros = FALSE)
}
\arguments{
\item{n}{A positive non-zero integer}
\item{len}{Either logical \code{TRUE}, or an integer less than or equal to
\code{n}. If the latter form is used then only those partions of length less
than or equal to len are returned}
\item{addZeros}{If true then the empty partitions are added to the list of
partitions.}
}
\value{
A list with each list element representing an integer partition
}
\description{
This function will return either all, or a length restricted subset of the
integer partitions of an integer n. The method works by considering
compositions rather than partions, hence the name.
}
\details{
This function will return all partions, or a subset, of an integer n. It
makes no check to see if this is a sensible thing to do. It also does it in
a lazy way in that in the restricted case it generates all partitions and
then only returns those that satistfy the length constraint. Users are
advised to check how many partitions are possible using partition number
function which is implemented the \code{P} function in the \pkg{partions}
package. Having said this P(50) is approximately 200 thousand, and P(100)
around 190 million, so the function should work well for smallish n.
}
\note{
This function does not warn the user that the requested set of
partitions may be very large. In addition, all working is handled entirely
in memory, and so this may cause it to crash if the request is
execeptionally large.
}
\examples{
## a small numeric example with all 11 partitions of 6
genComp(6)
## a small example with the integer partitions of 6 of length 3 with empty partitions added
genComp(6, 3, TRUE)
## a larger example - 627 partions of 20, but restricted to those of length 3 or smaller
genComp(20, 3)
}
\references{
Kelleher, J. (2005), Encoding Partitions As Ascending
Compositions, PhD thesis, University College Cork.
Kelleher, J. and O'Sullivan, B. (2009), Generating All Partitions: A
Comparison Of Two Encodings, \url{https://arxiv.org/abs/0909.2331}.
Kelleher, J. (2010) Generating Integer
Partitions,\url{https://jeromekelleher.net/tag/integer-partitions.html}.
}
\author{
Jerome Kelleher (algorithm and Python version) and James M. Curran
(C++ version/R interface)
}
\keyword{partitions}
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