how to get all subsets up to N in R

Question

I want to generate a list that contains all 2^n subsets of the numbers 1:N in R. How is the possible?

expand.grid( rep( list( 0:4), 2))

returns a data frame containing all the subsets of 0:4 size 2 - but i want a list, that contains all subsets of all sizes.

Answer 1

How about,

lapply(0:4, function(x) combn(4,x))
[[1]]
     [,1]

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

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

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

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

Answer 2

There is a set_power function in package sets that should return the power set which is the proper term from what your words are describing. You may want to revise you terminology, though, since your code is doing something different. expand.grid does not return mathematical sets but rather ordered combinations. In set theory {1,1} reduces to {1}. Expand grid does not do real set creation in that sense. If you wanted the list of all the data.frames up to length 4 that expand.grid could make, you can get that easily enough with:

lapply(0:4, function(n) expand.grid( rep( list( 0:4), n)) )