Perform 'cross product' of two vectors, but with addition

Question

I am trying to use R to perform an operation (ideally with similarly displayed output) such as

> x<-1:6
> y<-1:6
> x%o%y
     [,1] [,2] [,3] [         


        

Answer 1

expand.grid can answer your second question:

expand.grid(1:6,1:6)
expand.grid(1:6,1:6,1:4)

Answer 2

Your first question is easily handled by outer:

outer(1:6,1:6,"+")

For the others, I suggest you try expand.grid, although there are specialized combination and permutation functions out there as well if you do a little searching.