On the number of combinations without certain separations

Details On the number of combinations without certain separations On the number of combinations without certain separations

2008-05-09

arxiv.org/abs/0805.1276v1

European Journal of Combinatorics; V.29, Iss.5, July 2008, Pages 1200-1206

Mathematics

Combinatorics

Scientific paper

10.1016/j.ejc.2007.06.024

In this paper we enumerate the number of ways of selecting $k$ objects from $n$ objects arrayed in a line such that no two selected ones are separated by $m-1,2m-1,...,pm-1$ objects and provide three different formulas when $m,p\geq 1$ and $n\geq pm(k-1)$. Also, we prove that the number of ways of selecting $k$ objects from $n$ objects arrayed in a circle such that no two selected ones are separated by $m-1,2m-1,...,pm-1$ objects is given by $\frac{n}{n-pk}\binom{n-pk}{k}$, where $m,p\geq 1$ and $n\geq mpk+1$.

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