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    On Round-Robin Tournaments with a Unique Maximum Score and Some Related Results

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    2208.14932.pdf (217.4Kb)
    Links to Files
    https://arxiv.org/abs/2208.14932
    Permanent Link
    https://doi.org/10.48550/arXiv.2208.14932
    http://hdl.handle.net/11603/26168
    Collections
    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
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    Author/Creator
    Malinovsky, Yaakov
    Moon, John W.
    Author/Creator ORCID
    https://orcid.org/0000-0003-2888-674X
    Date
    2022-08-31
    Type of Work
    18 pages
    Text
    journal articles
    preprints
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Abstract
    Richard Arnold Epstein (1927-2016) published the first edition of ”The Theory of Gambling and Statistical Logic” in 1967. He introduced some material on roundrobin tournaments (complete oriented graphs) with n labeled vertices in Chapter 9; in particular, he stated, without proof, that the probability that there is a unique vertex with the maximum score tends to one as n tends to infinity. Our object here is to give a proof of this result along with some historical remarks and comments. We also give related results on pairs of equal scores and degrees in tournaments and graphs.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3544


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.