The grid shading problem is the problem of proving the unimodality of the sequence 
,
where for fixed 
and 
,
is the number of partitions of 
with at most 
parts and largest part at most 
. The grid shading problem was solved by Sylvester (1878) using
invariant theory (Proctor 1982). Proctor (1982) gave the first elementary proof of
this result.
The q-binomial coefficients give the generating function for this sequence.
