A new proof of a theorem of Mansour and Sun

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.Comment: 3 pages, to appear in European J. Combin., see also http://math.univ-lyon1.fr/~gu

On arithmetic partitions of Z_n

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.Comment: 10 pages, 1 figure, European J. Combin. (2008), doi:10.1016/j.ejc.2008.11.00