2015 USAMO Problems/Problem 4
Problem
Steve is piling 
indistinguishable stones on the squares of an 
grid. Each square can have an arbitrarily high pile of stones. After he finished piling his stones in some manner, he can then perform stone moves, defined as follows. Consider any four grid squares, which are corners of a rectangle, i.e. in positions 
for some 
, such that 
and 
. A stone move consists of either removing one stone from each of 
and 
and moving them to 
and 
respectively,j or removing one stone from each of and and moving them to and respectively.
Two ways of piling the stones are equivalent if they can be obtained from one another by a sequence of stone moves.
How many different non-equivalent ways can Steve pile the stones on the grid?
