"The Gale Ryser theorem asserts that if p1;p2 are two partitions of
n of respective lengths k1;k2 , then there is a binary k1Âk2 matrix
M such that p1 is the vector of row sums and p2 is the vector of
column sums of M , if and only if p2 dominates p1 ."
At the end it should say
"p2 conjugate (transpose) dominates p1"
The theorem is mis-stated yet the function seems to be working