On the number of combinations without certain separations

Authors:
Toufik Mansour;Yidong Sun
Affiliations:
Department of Mathematics, University of Haifa, 31905 Haifa, Israel;Department of Mathematics, Dalian Maritime University, 116026 Dalian, PR China
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

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=1 and n=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 nn-pk(n-pkk), where m,p=1 and n=mpk+1.