OP-00982 Open

A Sidorenko-type count for the Möbius ladder in abelian groups

Let $G$ be an abelian group of size $N$ and $A \subset G$ a set of density $\alpha$. Indices are taken modulo $5$. The question is very closely related to the case of Cayley graphs in the simplest open instance of Sidorenko's conjecture, the Möbius ladder $K_{5,5} \setminus C_{10}$.

Problem. Are there at least $\alpha^{15} N^{10}$ tuples $(x_1, \dots, x_5, y_1, \dots, y_5) \in G^{10}$ with $x_i + y_j \in A$ whenever $j \in \{i, i+1, i+2\}$?

Source: B. Green, 100 open problems (version of January 2026), Problem 12.

Imported from people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf.

Classification

Primary: CO — Combinatorics
Keywords: abelian groups, Cayley graphs, graph homomorphisms, Möbius ladder, Sidorenko's conjecture
Literature checked: Oct. 26, 2026 by clemens-admin

References

@article{sidorenko1993,
  author = {Sidorenko, Alexander},
  title = {A correlation inequality for bipartite graphs},
  journal = {Graphs and Combinatorics},
  volume = {9},
  number = {2-4},
  pages = {201--204},
  year = {1993},
  doi = {10.1007/BF02988307}
}

@misc{rossman2025mobius,
  author = {Rossman, Benjamin},
  title = {On {S}idorenko's conjecture for bipartite {M}{\"o}bius ladders},
  howpublished = {\url{https://users.cs.duke.edu/~br148/sidorenko-mobius.pdf}},
  year = {2025},
  note = {Note dated 8 May 2025}
}

@misc{green100open,
  author = {Green, Ben},
  title = {100 open problems},
  howpublished = {\url{https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf}},
  note = {Problem 12; version of January 2026, most recent update December 2025},
  year = {2026}
}

Citing this problem

This identifier is permanent. It will not change if the problem is solved, reclassified or withdrawn.

OP-00982, "A Sidorenko-type count for the Möbius ladder in abelian groups", clopen.solutions.