Permutation Pyramid

# creat a list of combinations and
# permutations of elements from
# a single vector. This requires
# a few libraries:
# library( dplyr )
# library( purrr ) 
# library( combinat ) 

# "order.matters" is means that 
# for every combination of elements
# find every order they can be
# arranged.

permutation.pyramid <- function( v, order.matters = TRUE ){

  # get the unique combinations of elements
  # and flatten them into a one dimensional list
  out <- 1:length(v) %>% 
    lapply(function( x ){ 
      combn( v, x ) %>% as.data.frame()
    }) %>% 
    purrr::flatten() %>% 
    unname()
  
  # if order.matters then find all the 
  # arrangements of each combination
  if( order.matters ){
    out <- out %>% 
      lapply(function( x ){
        combinat::permn( x )
      }) %>% 
      purrr::flatten()
  }
  
  # return list of permutations
  return( out )
} 

> test <- c("A","B","C")
> permutation.pyramid( test )
[[1]]
[1] "A"

[[2]]
[1] "B"

[[3]]
[1] "C"

[[4]]
[1] "A" "B"

[[5]]
[1] "B" "A"

[[6]]
[1] "A" "C"

[[7]]
[1] "C" "A"

[[8]]
[1] "B" "C"

[[9]]
[1] "C" "B"

[[10]]
[1] "A" "B" "C"

[[11]]
[1] "A" "C" "B"

[[12]]
[1] "C" "A" "B"

[[13]]
[1] "C" "B" "A"

[[14]]
[1] "B" "C" "A"

[[15]]
[1] "B" "A" "C"

> test <- c("A","B","C")
> permutation.pyramid( test, order.matters = FALSE )
[[1]]
[1] "A"

[[2]]
[1] "B"

[[3]]
[1] "C"

[[4]]
[1] "A" "B"

[[5]]
[1] "A" "C"

[[6]]
[1] "B" "C"

[[7]]
[1] "A" "B" "C"