Maximum-loneliness formulation of the Lonely Runner Conjecture
Maximum-loneliness formulation of the Lonely Runner Conjecture
Let be a set of distinct positive integers, and define the maximum loneliness by
where and denotes the distance to the nearest integer. Lonely Runner Conjecture, maximum-loneliness formulation. If are distinct positive integers, then
This is the succinct formulation obtained after translating one runner's speed to zero; it is equivalent to the Lonely Runner Conjecture for runners. The notation is attributed in the source to Kravitz, and the conjecture remains open.
Sources & referencesView supporting material
Primary source
Benjamin Bedert, “Riesz products and the Lonely Runner Conjecture: A wider gap of loneliness”, arXiv:2511.16636 (2025).
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