multinom {multicool}

R Documentation

Calculate multinomial coefficients

Description

This function calculates the number of permutations of a multiset, this being the multinomial coefficient. If a set X contains k unique elements x_1, x_2, \ldots, x_k with associate counts (or multiplicities) of n_1, n_2, \ldots, n_k, then this function returns

\frac{n!}{n_1!n_2!\ldots n_k!}

where n = \sum_{i=1}{k}n_i.

Usage

multinom(x, counts = FALSE)

Arguments

x	Either a multiset (with one or more potentially non-unique elements), or if counts is TRUE a set of counts of the unique elements of X. If counts is FALSE and x is not numeric, then x will be coerced into an integer vector internally. If counts is TRUE then x must be a vector of integers that are greater than, or equal to zero.
counts	if counts is TRUE, then this means x is the set of counts n_1, n_2, \ldots, n_k rather than the set itself

Details

multinom depends on C++ code written by Dave Barber which can be found at http://home.comcast.net/~tamivox/dave/multinomial/index.html. The code may require the STL algorithm library to be included in order to compile it.

Value

A single integer representing the multinomial coefficient for the given multiset, or given set of multiplicities.

Author(s)

James M. Curran, Dave Barber

References

http://home.comcast.net/~tamivox/dave/multinomial/index.html

Examples

## an example with a multiset X = (a,a,a,b,b,c)
## There are 3 a s, 2 b s and 1 c, so the answer should be
## (3+2+1)!/(3!2!1!) = 6!/3!2!1! = 60
x = rep(letters[1:3],3:1)
multinom(x)

## in this example x is a vector of counts
## the answer should be the same as above as x = c(3,2,1)
x = rep(letters[1:3],3:1)
x = as.vector(table(x)) #coerce x into a vector of counts
multinom(x, counts = TRUE)

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