PostgreSQL find all possible combinations (permutations) in recursive query
In a recursive query the terms in the search table that are used in an iteration are removed and then the query repeats with the remaining records. In your case that means that as soon as you have processed the first array element ("A") it is no longer available for further permutations of the array elements. To get those "used" elements back in, you need to cross-join with the table of array elements in the recursive query and then filter out array elements already used in the current permutation (position(t.i in cte.combo) = 0) and a condition to stop the iterations (ct <= 3).
WITH RECURSIVE t(i) AS ( SELECT * FROM unnest('{A,B,C}'::char[])), cte AS ( SELECT i AS combo, i, 1 AS ct FROM t UNION ALL SELECT cte.combo || t.i, t.i, ct + 1 FROM cte, t WHERE ct <= 3 AND position(t.i in cte.combo) = 0) SELECT ARRAY(SELECT combo FROM cte ORDER BY ct, combo) AS result;