On the number of combinations without certain separations

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dc.creatorMansour, Toufik
dc.creatorSun, Yidong
dc.date2008-05-09
dc.date.accessioned2026-07-07T09:37:58Z
dc.date.available2026-07-07T09:37:58Z
dc.descriptionIn 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 $n\geq mpk+1$.
dc.identifierhttps://arxiv.org/abs/0805.1276
dc.identifierhttp://arxiv.org/abs/0805.1276
dc.identifierEuropean Journal of Combinatorics; V.29, Iss.5, July 2008, Pages 1200-1206
dc.identifierdoi:10.1016/j.ejc.2007.06.024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160647
dc.subjectCombinatorics
dc.subject05A05;05A15
dc.titleOn the number of combinations without certain separations
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