IDEAS home Printed from https://ideas.repec.org/p/osf/osfxxx/w37fe.html
   My bibliography  Save this paper

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

Author

Listed:
  • Technology, Union County Academy For Information

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.

Suggested Citation

  • Technology, Union County Academy For Information, 2021. "Comparing the Rightmost Group Seat Number for K Groups of People Under Random Seating Assignment," OSF Preprints w37fe, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:w37fe
    DOI: 10.31219/osf.io/w37fe
    as

    Download full text from publisher

    File URL: https://osf.io/download/601b608bfb09cd00567651ae/
    Download Restriction: no
    File URL: https://libkey.io/10.31219/osf.io/w37fe?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. agarwal, shekhar & Dutta, Madhurima & Dutta, Ritvik & Krishna, Vijesh, 2022. "Leveraging Artificial Intelligence in the Cyber Workplace: Prospects and Limitations for the Cyber Economy," Thesis Commons 4yr8j, Center for Open Science.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:osf:osfxxx:w37fe. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: OSF (email available below). General contact details of provider: https://osf.io/preprints/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.