[GENERAL] Ordering of window functions with no order specified?

In this particular case, I'm wondering about row_number(), and whether I explicitly need to repeat the ordering that's already specified in the query?

SELECT a,b,c,row_number()

OVER (PARTITION BY a) -- Do I need an ORDER BY c,b here?

FROM foo

ORDER  BY c,b

Also, I'm interested in both what if any behavior is guaranteed, and what gets done in practice.  (i.e., a SELECT with no order doesn't have guarantees, but in practice seems to return the results in the order they were added to the table.  Is it something similar here?)

Thanks!

Ken

--