Could/would you mind describing or listing the respective complements and causalities of the Northern and Lannister forces at the Battle on the Green Fork? I seem to be seeing a good deal of discrepancy on the topic.

So we know Bolton goes into the Battle of the Green Fork with ~17,000 men, and has around 10,000 during the time of the Battle of the Fords, suggesting around 6-7,000 casualties.

As for Tywin’s army, there’s this weird thing where it seems to be around 20,000 forever despite taking casualties. My calculations is that between the Battle of the Green Fork and the forced march that followed, I think Tywin lost at least 3,000 men.