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PreprintarXiv licencearXiv

A Counterexample to the Gyarmati-Matolcsi-Ruzsa Conjecture

  • Chandra Nair
  • Aref Namayandeh
  • Zhaobang Zhu
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Abstract

We provide a counterexample to the non-abelian Gyarmati-Matolcsi-Ruzsa conjecture. The construction comes from an equivalent maximal-coupling entropy inequality, for which a counterexample can be found in a lower-dimensional group. We give an explicit cardinality counterexample in D414, the fourteenth direct power of the dihedral group of order $8$.

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Cite

BibTeXRIS
BibTeX
@misc{nair2026counterexample,
  title = {{A Counterexample to the Gyarmati-Matolcsi-Ruzsa Conjecture}},
  author = {Chandra Nair and Aref Namayandeh and Zhaobang Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00156},
  eprint = {2611.00156},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00156},
}
RIS
TY  - UNPB
TI  - A Counterexample to the Gyarmati-Matolcsi-Ruzsa Conjecture
AU  - Chandra Nair
AU  - Aref Namayandeh
AU  - Zhaobang Zhu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00156
UR  - https://arxiv.org/abs/2611.00156
AB  - We provide a counterexample to the non-abelian Gyarmati-Matolcsi-Ruzsa conjecture. The construction comes from an equivalent maximal-coupling entropy inequality, for which a counterexample can be found in a lower-dimensional group. We give an explicit cardinality counterexample in D_4^14, the fourteenth direct power of the dihedral group of order $8$.
ER  -