On arithmetic partitions of

Generalizing a classical problem in enumerative combinatorics, Mansour and Sun counted the number of subsets of Z n without certain separations. Chen, Wang, and Zhang then studied the problem of partitioning Z n 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.