On arithmetic partitions of Z_n

Abstract

Generalizing a classical problem in enumerative combinatorics, Mansour and Sun counted the number of subsets of ${\mathbb{Z}}_n$ without certain separations. Chen, Wang, and Zhang then studied the problem of partitioning ${\mathbb{Z}}_n$ 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.

10 pages, 1 figure, European J. Combin. (2008), doi:10.1016/j.ejc.2008.11.009

References in corpus (2)

• On the number of combinations without certain separations
• A new proof of a theorem of Mansour and Sun