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Hamilton Decompositions of the Directed 5-Torus, Odd Modulus

Combinatorics · solved

1 attempt

Statement

The directed five-dimensional torus D5(m)D_5(m) has a Hamilton decomposition for every odd m≥3m \geq 3, extending the decomposition program for directed tori beyond the three-dimensional case.

Context

A concrete decomposition question with a one-paper audience, sibling to the directed 3-torus entry already in the catalog.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.5 Pro, GPT-5.5 Codex, Claude Opus 4.7 with SangHyun Park ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro, GPT-5.5 Codex, Claude Opus 4.7
    people
    SangHyun Park

    GPT-5.5 Pro "contributed to proof exploration, including selector design and block-recurrence case analysis"; GPT-5.5 Codex drafted the Lean 4 formalization; Claude Opus 4.7 contributed exposition. All mathematical content author-verified.

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