More lacunary partition functions
Let \(Q_{m,k}(n)\) denote the number of partitions of \(n\) into distinct parts \(\lambda_i\) such that (i) each \(\lambda_i\equiv 0\), \(m\pmod k\); (ii) the least part \(\lambda_1\equiv 0\pmod k\); (iii) \(2\lambda_1+ m\) does not occur as a part. Let \(Q_{m,k}^{\pm}(n)\) denote respectively the number of such partitions into evenly, oddly many parts. The author's main result is that \(Q^+_{m,k}(n)- Q^-_{m,k}(n)\) is lacunary.
scientific article; zbMATH DE number 1993671