On arithmetic partitions of ZnZn

Generalizing a classical problem in enumerative combinatorics, Mansour and Sun counted the number of subsets of ZnZn without certain separations. Chen, Wang, and Zhang then studied the problem of partitioning ZnZn into arithmetical progressions of a given type under some technical conditions. In this paper, we improve on their main theorems by applying a convolution formula for cyclic multinomial coefficients due to Raney–Mohanty.