Here is a question for more elegant programming:

pj = {j - 1, j, j + 1}

pi = {i - 1, i, i + 1}

pk = {k - 1, k, k + 1}

I want to combine these three lists which have three elements each, in such a way that each element of one list is combined with one element of all remaining lists. When I use Partition, Flatten and Table Commands, the result looks like

pt = Partition[
  Flatten[Table[{i + (u1 - 2), j + (u2 - 2), k + (u3 - 2)}, {u1, 1, 
     3}, {u2, 1, 3}, {u3, 1, 3}]], 3]

{{-1 + i, -1 + j, -1 + k}, {-1 + i, -1 + j, k}, {-1 + i, -1 + j, 
  1 + k}, {-1 + i, j, -1 + k}, {-1 + i, j, k}, {-1 + i, j, 
  1 + k}, {-1 + i, 1 + j, -1 + k}, {-1 + i, 1 + j, k}, {-1 + i, 1 + j,
   1 + k}, {i, -1 + j, -1 + k}, {i, -1 + j, k}, {i, -1 + j, 
  1 + k}, {i, j, -1 + k}, {i, j, k}, {i, j, 1 + k}, {i, 
  1 + j, -1 + k}, {i, 1 + j, k}, {i, 1 + j, 
  1 + k}, {1 + i, -1 + j, -1 + k}, {1 + i, -1 + j, k}, {1 + i, -1 + j,
   1 + k}, {1 + i, j, -1 + k}, {1 + i, j, k}, {1 + i, j, 
  1 + k}, {1 + i, 1 + j, -1 + k}, {1 + i, 1 + j, k}, {1 + i, 1 + j, 
  1 + k}}

Length[pt]
27

Now, I want to combine n lists (p1, p2, ..., pn), which have three elements each in the way described above. The resulting list is a {3^n, n} matrix. I am looking for an elegant solution.

Best,

GG