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An $\ell$-Oddtown is a family of subsets of an $n$-element set whose set sizes are not divisible by $\ell$ while all pairwise intersection sizes are. Berlekamp and Graver showed the maximum size is $n$ for prime $\ell$, Babai and Frankl extended this to prime powers and asked whether $n$ still holds for other moduli, a question open even for $\ell = 6$. Bukh, Chao and Zheng answer it negatively with an explicit superlinear construction, complemented by new upper bounds.
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The lower-bound construction in Section 2 was first proposed by GPT-5.6 Sol in response to prompts from the authors; the upper-bound results were obtained without AI assistance. (The disclosure was added in the paper's second version.)
Provider: OpenAI · Prompt public: unknown · Independence: unknown
No verification note supplied.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.