Creating permutations and combinations with replacement

gtools

library(gtools)

## Combination with replacement
res.comb <- combinations(n = 2, r = 4, v = c("●","○"), repeats.allowed = TRUE)
print(res.comb, quote = FALSE)

     [,1] [,2] [,3] [,4]
[1,] ○    ○    ○    ○   
[2,] ○    ○    ○    ●   
[3,] ○    ○    ●    ●   
[4,] ○    ●    ●    ●   
[5,] ●    ●    ●    ●   

## Permutation with replacement
res.perm <- permutations(n = 2, r = 4, v = c("●","○"), repeats.allowed = TRUE)
print(res.perm, quote = FALSE)

      [,1] [,2] [,3] [,4]
 [1,] ○    ○    ○    ○   
 [2,] ○    ○    ○    ●   
 [3,] ○    ○    ●    ○   
 [4,] ○    ○    ●    ●   
 [5,] ○    ●    ○    ○   
 [6,] ○    ●    ○    ●   
 [7,] ○    ●    ●    ○   
 [8,] ○    ●    ●    ●   
 [9,] ●    ○    ○    ○   
[10,] ●    ○    ○    ●   
[11,] ●    ○    ●    ○   
[12,] ●    ○    ●    ●   
[13,] ●    ●    ○    ○   
[14,] ●    ●    ○    ●   
[15,] ●    ●    ●    ○   
[16,] ●    ●    ●    ●   

## Reformat
res.perm <- apply(res.perm,  MARGIN = 1, paste, collapse = " ")
res.perm <- data.frame(perm = res.perm)
print(res.perm, row.names = FALSE)

    perm
 ○ ○ ○ ○
 ○ ○ ○ ●
 ○ ○ ● ○
 ○ ○ ● ●
 ○ ● ○ ○
 ○ ● ○ ●
 ○ ● ● ○
 ○ ● ● ●
 ● ○ ○ ○
 ● ○ ○ ●
 ● ○ ● ○
 ● ○ ● ●
 ● ● ○ ○
 ● ● ○ ●
 ● ● ● ○
 ● ● ● ●

Create permutations of different sizes

size <- 5

list.perm <- lapply(seq_len(size), function(i) {

    permutations(n = 2, r = i, v = c("●","○"), repeats.allowed = TRUE)
})

library(plyr)
l_ply(list.perm, print, quote = F)

     [,1]
[1,] ○   
[2,] ●   
     [,1] [,2]
[1,] ○    ○   
[2,] ○    ●   
[3,] ●    ○   
[4,] ●    ●   
     [,1] [,2] [,3]
[1,] ○    ○    ○   
[2,] ○    ○    ●   
[3,] ○    ●    ○   
[4,] ○    ●    ●   
[5,] ●    ○    ○   
[6,] ●    ○    ●   
[7,] ●    ●    ○   
[8,] ●    ●    ●   
      [,1] [,2] [,3] [,4]
 [1,] ○    ○    ○    ○   
 [2,] ○    ○    ○    ●   
 [3,] ○    ○    ●    ○   
 [4,] ○    ○    ●    ●   
 [5,] ○    ●    ○    ○   
 [6,] ○    ●    ○    ●   
 [7,] ○    ●    ●    ○   
 [8,] ○    ●    ●    ●   
 [9,] ●    ○    ○    ○   
[10,] ●    ○    ○    ●   
[11,] ●    ○    ●    ○   
[12,] ●    ○    ●    ●   
[13,] ●    ●    ○    ○   
[14,] ●    ●    ○    ●   
[15,] ●    ●    ●    ○   
[16,] ●    ●    ●    ●   
      [,1] [,2] [,3] [,4] [,5]
 [1,] ○    ○    ○    ○    ○   
 [2,] ○    ○    ○    ○    ●   
 [3,] ○    ○    ○    ●    ○   
 [4,] ○    ○    ○    ●    ●   
 [5,] ○    ○    ●    ○    ○   
 [6,] ○    ○    ●    ○    ●   
 [7,] ○    ○    ●    ●    ○   
 [8,] ○    ○    ●    ●    ●   
 [9,] ○    ●    ○    ○    ○   
[10,] ○    ●    ○    ○    ●   
[11,] ○    ●    ○    ●    ○   
[12,] ○    ●    ○    ●    ●   
[13,] ○    ●    ●    ○    ○   
[14,] ○    ●    ●    ○    ●   
[15,] ○    ●    ●    ●    ○   
[16,] ○    ●    ●    ●    ●   
[17,] ●    ○    ○    ○    ○   
[18,] ●    ○    ○    ○    ●   
[19,] ●    ○    ○    ●    ○   
[20,] ●    ○    ○    ●    ●   
[21,] ●    ○    ●    ○    ○   
[22,] ●    ○    ●    ○    ●   
[23,] ●    ○    ●    ●    ○   
[24,] ●    ○    ●    ●    ●   
[25,] ●    ●    ○    ○    ○   
[26,] ●    ●    ○    ○    ●   
[27,] ●    ●    ○    ●    ○   
[28,] ●    ●    ○    ●    ●   
[29,] ●    ●    ●    ○    ○   
[30,] ●    ●    ●    ○    ●   
[31,] ●    ●    ●    ●    ○   
[32,] ●    ●    ●    ●    ●