3 research outputs found
On arithmetic partitions of Z_n
Generalizing a classical problem in enumerative combinatorics, Mansour and
Sun counted the number of subsets of without certain separations. Chen,
Wang, and Zhang then studied the problem of partitioning 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
The number of s-separated k-sets in various circles
This article studies the number of ways of selecting k objects arranged in p circles of sizes n0,...,np−1 such that no two selected ones have less than s objects between them. If ni ≥ sk + 1 for all 0 ≤ i ≤ p − 1, this number is shown to be n0+...+np−2 k n0+...+np−2−sk−1 k−1 . A combinatorial proof of this claim is provided, and two convolution formulas due to Rothe are obtained as corollaries.Fil: Estrugo, Emiliano Juan José. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Pastine, Adrián Gabriel. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentin