Comparing the Rightmost Group Seat Number for K Groups of People Under Random Seating Assignment

Union County Academy For Information Technology

No w37fe, OSF Preprints from Center for Open Science

Abstract: Suppose there are $N$ seats labeled 1 to $N$ from left to right. There are $K$ groups of people that need to be seated. Denote the rightmost seating number of each group by $M_1, M_2, \ldots, M_K$. This article studies the probability that a group $k$ has the smallest value among $\{M_l, l=1,\ldots,K\}$ and its relationship with the group sizes $L_1,L_2, \ldots, L_K$. In particular, it is shown that when the groups are non-overlapping, the group with the fewest number of people tends to have the smallest rightmost value of $M_k$. This result can be generalized to the case of overlapping groups under some assumptions. However, the result does not generalize to all cases and we demonstrate this with counterexamples.

Date: 2021-02-03
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:w37fe

DOI: 10.31219/osf.io/w37fe

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