Enumerazione delle partizioni della tabella nella tabella di Postgres

Sì, è semplice:

SELECT id, part, value,
       row_number() OVER (PARTITION BY grp ORDER BY id) - 1 AS number
FROM (SELECT id, part, value,
             sum(part) OVER (ORDER BY id) AS grp
      FROM mytable
     ) AS q;

 id | part | value | number 
----+------+-------+--------
  1 |    0 |     8 |      0
  2 |    0 |     3 |      1
  3 |    0 |     4 |      2
  4 |    1 |     6 |      0
  5 |    0 |    13 |      1
  6 |    0 |     4 |      2
  7 |    1 |     2 |      0
  8 |    0 |    11 |      1
  9 |    0 |    15 |      2
 10 |    0 |     3 |      3
 11 |    0 |     2 |      4
(11 rows)