Another way to count colored Frobenius partitions (Q2782412)

Let \(c\varphi_k (n,m)\) denote the number of generalized Frobenius partitions on \(n\), using \(k\) colors, and whose color difference is \(m\). Using generating functions, the author obtains results such as the following: NEWLINENEWLINENEWLINETheorem 2.1: If \(k\) is even and \(c= (4l^3-l)/3\), then \(c\varphi_k (n+2m+c, m+c)= c\varphi_k (n,m)\). NEWLINENEWLINENEWLINETheorem 2.2: If \(k\) is odd, \(k>1\), and \(d= l(l+1)(2l+1)/6\), then \(c\varphi_k (n+m+d, m+2d)= c\varphi_k (n,m)\).NEWLINENEWLINEFor the entire collection see [Zbl 0980.00024].