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Kourovka Problem 18.50 - Prescribed Permuted-Product Cardinality

Algebra · posed by 2014 · solved

2 comments

Statement

Given nn and 1≤c≤n!1 \le c \le n!, can nn distinct group elements be chosen so that their n!n! ordered products take exactly cc distinct values? Constructions realize every cc.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Aristotle

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    The solution was discovered autonomously by Aristotle and formalized in Lean; the human authors curated the exposition.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Autonomously discovered and formally verified in Lean by Aristotle; author-curated arXiv preprint covering eight Kourovka Notebook problems.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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