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The Small Davenport Constant of the Heisenberg Group of Order 125

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davenport-constant-heisenberg-125Combinatoricsposed by Godara and Sarkarrecorded: solved

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Statement

Godara and Sarkar proved d(H27)=6\mathsf{d}(H_{27})=6 for the exponent-pp Heisenberg group and posed d(Hp3)=3p−3\mathsf{d}(H_{p^3})=3p-3 for every odd prime pp, leaving p≥5p\ge5 open. The paper settles the first open case, d(H125)=12\mathsf{d}(H_{125})=12, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.

Context

Settles the case p=5. The posed formula for every odd prime remains open.

First open case of a posed formula in zero-sum theory over non-abelian groups.

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  • #1

    Attempt 1

    computationClaude + GPT-5 with Patrick White ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Claude + GPT-5
    people
    Patrick White

    An attribution note states the results were obtained by an AI research collaboration in which an AI system occupied the principal research seat under human direction. Claude produced the search implementations, the independent reproduction of the load-bearing computation and the write-up; a tool-free GPT-5 produced the reduction to the lemma chain and the corrected hypotheses of several lemmas.

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