Translative covering densities of order n log n
For every sufficiently large dimension n , we construct a centrally symmetric convex body whose translative covering density exceeds $c n\log n$, where c > 0 is absolute. This disproves the existence of a universal linear upper bound and matches the order of Rogers' upper bound.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
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