On the number of combinations without certain separations

Toufik Mansour, Yidong Sun

Research output: Contribution to journalArticlepeer-review

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, 2 m - 1, ..., p m - 1 objects and provide three different formulas when m, p ≥ 1 and n ≥ p m (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, 2 m - 1, ..., p m - 1 objects is given by frac(n, n - p k) (frac(n - p k, k)), where m, p ≥ 1 and n ≥ m p k + 1.

Original languageEnglish
Pages (from-to)1200-1206
Number of pages7
JournalEuropean Journal of Combinatorics
Volume29
Issue number5
DOIs
StatePublished - Jul 2008

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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