Distribution of the full rank in residue classes for odd moduli

The distribution of values of the full ranks of marked Durfee symbols is examined in prime and nonprime arithmetic progressions. The relative populations of different residues for the same modulus are determined: the primary result is that k -marked Durfee symbols of n equally populate the residue classes a and b mod 2 k + 1 if g c d ( a , 2 k + 1 ) = g c d ( b , 2 k + 1 ) . These are used to construct a few congruences. The general procedure is illustrated with a particular theorem on 4-marked symbols for multiples of 3.