set-returning functions in postgres I've been trying to use the generate_series() function of Postgres to obtain a a table like this:



I didn't arrived to a solution yet, so any ideas would be appreciated.
I guess something like this would do:

select x.n, y.n 
from generate_series(1,3) as x(n) 
cross join generate_series(1,4) as y(n)
order by y.n, x.n


The idea is to take the Cartesian product between a set of 3 elements and a set with 4 elements. In this case Z_3 and Z_4

Since 3 and 4 is co-prime ( gcd(3,4) = 1 ), we can conclude that the Cartesian product between Z_3 and Z_4 is isomorphic with Z_12 (if only we had formatting options ...). See zm-cross-zn-isomorphic-to-zmn for a proof. I.e we can use Z_12 and use modulo arithmetic to achieve the desired set:

select mod(x.n,3)+1, mod(x.n,4)+1 
from generate_series(1,12) as x(n) 
order by mod(x.n,4)+1, mod(x.n,3)+1