About a combinatorial problem with n seats and n people

2023/03/31 by Simon Wundling, Wundling, Simon
Engineering · Mathematics · #Advanced Manufacturing and Logistics Optimization #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics #Urban Design and Spatial Analysis

paper · pdf · doi:10.48550/arxiv.2303.18175

openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If you want to fill n ∈ ℕ seats in succession with n people and the rule that each person chooses one of the seats with the maximum distance to an occupied seat, then you can ask yourself how many possibilities there are for this. In this paper, based on initially mentioned ideas, a formula for the number of these possibilities will be found. In addition, a lower and upper bound for this formula will be given. Finally, formulas for the OEIS sequences A166079, A095236, A095240 and A095912 and an extension of the initial problem are derived.

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