Explicit counterexamples disprove the shifted Lonely Runner Conjecture for n=5 and the Lonely Vector Property for n=12 by introducing coloopless zonotopes.
Nine and ten lonely runners
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The Lonely Runner Conjecture of Wills and Cusick states that if $k+1$ runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least $1/(k+1)$ away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for $8$ runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for $9$ and $10$ runners.
years
2026 2representative citing papers
Introduces the mixed lonely runner property MLPS_k and exactly characterizes MLPS_2 while deriving Fourier-based summation and integral formulas for unequal thresholds.
citing papers explorer
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Coloopless zonotopes and counterexamples to the Shifted Lonely Runner Conjecture
Explicit counterexamples disprove the shifted Lonely Runner Conjecture for n=5 and the Lonely Vector Property for n=12 by introducing coloopless zonotopes.
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Mixed thresholds in the Lonely Runner Conjecture
Introduces the mixed lonely runner property MLPS_k and exactly characterizes MLPS_2 while deriving Fourier-based summation and integral formulas for unequal thresholds.