FURTHER RESULTS ON BIASES IN INTEGER PARTITIONS

摘要

Let P-a,P-b,P-m (n) be the number of integer partitions of n with more parts congruent to a modulo m than parts congruent to b modulo m. We prove that p(a,b,m) (n) >= P-b,P-a,P-m (n) whenever 1 <= a <= b <= m. We also propose some conjectures concerning series with nonnegative coefficients in their expansions.