Old and new moving-knife schemes

Steven J. Brams, Alan D. Taylor, William S. Zwicker

    Research output: Contribution to journalArticle

    Abstract

    In general, moving-knife schemes seem to be easier to come by than pure existence results (like Neyman's [N] theorem) but harder to come by than discrete algorithms (like the Dubins-Spanier [DS] last-diminisher method). For envy-free allocations for four or more people, however, the order of difficulty might actually be reversed. Neyman's existence proof (for any n) goes back to 1946, the discovery of a discrete algorithm for all n ≥ 4 is quite recent [BT1, BT2, BT3], and a moving-knife solution for n = 4 was found only as this article was being prepared (see [BTZ]). We are left with this unanswered question: Is there a moving-knife scheme that yields an envyfree division for five (or more) players?

    Original languageEnglish (US)
    Pages (from-to)30-35
    Number of pages6
    JournalThe Mathematical Intelligencer
    Volume17
    Issue number4
    DOIs
    StatePublished - Dec 1995

    ASJC Scopus subject areas

    • Mathematics(all)
    • History and Philosophy of Science

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  • Cite this

    Brams, S. J., Taylor, A. D., & Zwicker, W. S. (1995). Old and new moving-knife schemes. The Mathematical Intelligencer, 17(4), 30-35. https://doi.org/10.1007/BF03024785