The number of s-separated k-sets in various circles

2018/05/03 by Estrugo, Emiliano J. J., Pastine, Adrián
#05A15 05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.01562

Abstract

This article studies the number of ways of selecting k objects arranged in p circles of sizes n₁,…,n_p such that no two selected ones have less than s objects between them. If n_i≥ sk+1 for all 1≤ i ≤ p, this number is shown to be (n₁+…+n_p)/(k)\binomn₁+…+n_p-sk-1k-1. A combinatorial proof of this claim is provided, and some nice combinatorial formulas are derived.

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