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Erdős-Herzog-Piranian Distance Products: Improved Lower Bound

Combinatorics · posed by Paul Erdős, Fritz Herzog, George Piranian, 1958 · partial

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Erdős, Herzog and Piranian (1958) asked whether the regular n-gon maximizes the product of pairwise distances among n points of fixed diameter. After the recent discovery that it does not for even n, this paper proves the first exponential improvement over the n-gon's value, via a vector-field technique.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Nat Sothanaphan, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The acknowledgments thank "Stijn Cambie, ChatGPT, and Quanyu Tang for discussion (in alphabetical order)" - a discussion credit, listed alongside the human colleagues, with no specific step attributed.

    An improved lower bound on the maximal product; the sharp maximizer for the 1958 question remains unknown.

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