Babai and Frankl's Oddtown Question for Composite Moduli
Statement
An -Oddtown is a family of subsets of an -element set whose set sizes are not divisible by while all pairwise intersection sizes are. Berlekamp and Graver showed the maximum size is for prime , Babai and Frankl extended this to prime powers and asked whether still holds for other moduli, a question open even for . Bukh, Chao and Zheng answer it negatively with an explicit superlinear construction, complemented by new upper bounds.
Record
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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Boris Bukh, Ting-Wei Chao and Zeyu Zheng, using GPT-5.6 SolThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.)
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