Combinaciones de PostgreSQL sin repeticiones

set search_path='tmp';

WITH ztab AS (
SELECT idx as idx
, substring ( 'WTF!' FROM idx FOR 1) as str
FROM generate_series(1, char_length( 'WTF!' )) idx
)
SELECT t1.str, t2.str
FROM ztab t1
JOIN ztab t2 ON t2.idx > t1.idx
        ;

Resultado:

 str | str 
-----+-----
 W   | T
 W   | F
 W   | !
 T   | F
 T   | !
 F   | !
(6 rows)

Desafortunadamente, no puedo encontrar una manera de evitar la constante de doble cadena. (pero todo podría empaquetarse en una función) Si no hay caracteres duplicados (o si desea suprimirlos), puede hacer el anti-join en str en lugar de idx.

ACTUALIZAR (sugerencia de ypercube) Parece que el OP quiere que las cadenas se concatenen. Así sea::

WITH ztab AS (
SELECT idx as idx
, substring ( 'WTF!' FROM idx FOR 1) as str
FROM generate_series(1, char_length( 'WTF!' )) idx
)
SELECT t1.str || t2.str AS results
FROM ztab t1
JOIN ztab t2 ON t2.idx > t1.idx
        ;

Resultados:

 results 
---------
 WT
 WF
 W!
 TF
 T!
 F!
(6 rows)

ACTUALIZACIÓN 2:(aquí viene la cosita recursiva...)

WITH RECURSIVE xtab AS (
        WITH no_cte AS (
        SELECT
        1::int AS len
        , idx as idx
        , substring ( 'WTF!' FROM idx FOR 1) as str
        FROM generate_series(1, char_length( 'WTF!' )) idx
        )
        SELECT t0.len as len
                , t0.idx
                , t0.str
        FROM no_cte t0
        UNION SELECT 1+t1.len
                , tc.idx
                , t1.str || tc.str AS str
        FROM xtab t1
        JOIN no_cte tc ON tc.idx > t1.idx
        )
SELECT * FROM xtab
ORDER BY len, str
-- WHERE len=2
        ;

Resultados 3:

 len | idx | str  
-----+-----+------
   1 |   4 | !
   1 |   3 | F
   1 |   2 | T
   1 |   1 | W
   2 |   4 | F!
   2 |   4 | T!
   2 |   3 | TF
   2 |   4 | W!
   2 |   3 | WF
   2 |   2 | WT
   3 |   4 | TF!
   3 |   4 | WF!
   3 |   4 | WT!
   3 |   3 | WTF
   4 |   4 | WTF!
(15 rows)