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Optimal Partial Plank Coverings

Geometry & topology · posed by Karoly Bezdek · solved

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Statement

Given planks of fixed total width, how should they be placed to cover as much of a convex body's volume as possible? Karoly Bezdek asked whether, for a Euclidean ball, the optimum is a single plank centred at the origin. It is, and the paper also settles every planar convex body.

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

  1. proof attempt · #1

    Egor Bakaev and Alexander Polyanskii, 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 paper credits iterative discussions between the authors and ChatGPT with the proof of concavity of Minkowski subtraction - explicitly within the authors' own existing Minkowski-subtraction approach - and with the idea for the planar case. The overall approach is the authors'.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.