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In basketball, to assume an offensive position between the free throw lane ("the paint") and the basket (an area known as the low post) with one's back to the basket and a defending player, so as to receive the ball in a position where one can attempt to shoot or move closer to the basket. If you've got a size advantage, post up and I'll get the ball to you.
post something up
to record a transaction in an account. I'll post this charge up right away, and then you can check out. Please post up the charges a little later.