A. Christopher

Combinatorial and arithmetic properties of nr-partitions: A unified analytic generalization

This paper presents a comprehensive study of $n^r$-partitions, defined by the generating function $\prod_{n=1}^{\infty} (1 - q^n)^{-n^r}$, which interpolates analytically between ordinary partitions ($r=0$), plane partitions ($r=1$), and higher-dimensional combinatorial structures ($r\geq2$). Our main contributions in...