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A hypercontractive proof of the sharp bound for cancellative pairs

  • Fan Chang
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Abstract

Fang and Huang proved that every cancellative pair (π’œ,ℬ) of families of subsets of [n] satisfies |π’œ|Β·|ℬ|≀(9/4)n. Their proof uses entropy. We give a Fourier-analytic proof based on Lifshitz's one-sided noise operator T1/4β†’1/2. The main tool is a near-L1 hypercontractive estimate for this operator.

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Cite

BibTeXRIS
BibTeX
@misc{chang2026hypercontractive,
  title = {{A hypercontractive proof of the sharp bound for cancellative pairs}},
  author = {Fan Chang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09105},
  eprint = {2609.09105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09105},
}
RIS
TY  - UNPB
TI  - A hypercontractive proof of the sharp bound for cancellative pairs
AU  - Fan Chang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09105
UR  - https://arxiv.org/abs/2609.09105
AB  - Fang and Huang proved that every cancellative pair (π’œ,ℬ) of families of subsets of [n] satisfies |π’œ|Β·|ℬ|≀(9/4)^n. Their proof uses entropy. We give a Fourier-analytic proof based on Lifshitz's one-sided noise operator T^1/4β†’1/2. The main tool is a near-L^1 hypercontractive estimate for this operator.
ER  -