I found this function in R that can return the "power set" for a set of letters:

```
f <- function(set) {
n <- length(set)
masks <- 2^(1:n-1)
lapply( 1:2^n-1, function(u) set[ bitwAnd(u, masks) != 0 ] )
}
results = f(LETTERS[1:3])
[[1]]
character(0)
[[2]]
[1] "A"
[[3]]
[1] "B"
[[4]]
[1] "A" "B"
[[5]]
[1] "C"
[[6]]
[1] "A" "C"
[[7]]
[1] "B" "C"
[[8]]
[1] "A" "B" "C"
```

As an example, suppose I were to generate some random sequence of letters:

```
> random = sample.int(length(results), 1)
[1] 6
> results[random]
[[1]]
[1] "A" "C"
```

Suppose now I want to make a list of the power set for all 26 letters: I know that this list would have 2^26 = 67108864 elements. There is no way that I would be able to store such a large list in the local R environment!

```
# too big
big_results = f(LETTERS[1:26])
```

But suppose I were to generate some random number:

```
big_random = sample.int(67108864, 1)
13626980
```

- Is there some way of knowing which permutation of letters the "big_random" would correspond to on the "big_results" list - without actually fully running "big_results"?

For example:

```
# too big to run (hypothetical list)
big_results[big_random]
```

- Could some enumeration or recursion formula be used to figure out some pattern and then somehow determine that "13626980" corresponds to the letters "P H R T L D U Z" for instance?

Thank you!