Combinatorics using R

Using the combinat Package

Download the combinat package from CRAN using RStudio or the install.packages() command. Then load the combinat library.

library(combinat)

## 
## Attaching package: 'combinat'

## The following object is masked from 'package:utils':
## 
##     combn

Examples:

1. Permutations of 1, 2, 3.

permn(3)   #use the highest value

## [[1]]
## [1] 1 2 3
## 
## [[2]]
## [1] 1 3 2
## 
## [[3]]
## [1] 3 1 2
## 
## [[4]]
## [1] 3 2 1
## 
## [[5]]
## [1] 2 3 1
## 
## [[6]]
## [1] 2 1 3

length(permn(3))   #count the number of permutations

## [1] 6

2. Permutations of the words circle, square, and triangle.

x <- c("circle", "square", "triangle")
permn(x)

## [[1]]
## [1] "circle"   "square"   "triangle"
## 
## [[2]]
## [1] "circle"   "triangle" "square"  
## 
## [[3]]
## [1] "triangle" "circle"   "square"  
## 
## [[4]]
## [1] "triangle" "square"   "circle"  
## 
## [[5]]
## [1] "square"   "triangle" "circle"  
## 
## [[6]]
## [1] "square"   "circle"   "triangle"

length(permn(x))   #count the number of permutations

## [1] 6

3. Combinations of 1, 2, 3, 4 taken 3 at a time.

combn(4,3)

##      [,1] [,2] [,3] [,4]
## [1,]    1    1    1    2
## [2,]    2    2    3    3
## [3,]    3    4    4    4

ncol(combn(4,3))   #count the number of combinations

## [1] 4

4. Combinations of the words circle, square, and triangle taken 2 at a time.

x <- c("circle", "square", "triangle")
combn(x, 2)

##      [,1]     [,2]       [,3]      
## [1,] "circle" "circle"   "square"  
## [2,] "square" "triangle" "triangle"

ncol(combn(x, 2))   #count the number of combinations

## [1] 3

Another package in R that can be used in combinatorics is the gtools package. This is useful when you want to specify if repetition is allowed or not allowed.

Using the gtools Package

Download the gtools package from CRAN using RStudio or the install.packages() command. Then load the gtools library.

library(gtools)

Examples:

1. Permutations of 39 taken 4 at a time were repetition is allowed.

x <- nrow(permutations(n=39, r=4, repeats.allowed=T))
print(x)

## [1] 2313441

2. Combinations of the letters from J to M taken 2 at a time where repetition is not allowed.

x <- c("J", "K", "L", "M")
y <- nrow(combinations(n=4, r=2, v=x, repeats.allowed=F))
print(y)

## [1] 6