Distribution of the full rank in residue classes for odd moduli

Details Distribution of the full rank in residue classes for odd moduli Distribution of the full rank in residue classes for odd moduli

2009-05-22

arxiv.org/abs/0905.3761v1

Mathematics

Combinatorics

9 pages, no figures

Scientific paper

10.1016/j.disc.2009.02.032

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 2k+1 if gcd(a,2k+1)=gcd(b,2k+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.

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