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.
