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Note on Robins’ conjecture in dimension four and higher
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 29 May 2026, pp. 1-6
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This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-tilers must coincide up to rigid motions if and only if their Fourier transforms agree on the lattice $\mathbb {Z}^d$
. In this article, we disprove the conjecture by constructing explicit counterexamples in dimensions $d \geq 4$
.
