Explicit counterexamples disprove the shifted Lonely Runner Conjecture for n=5 and the Lonely Vector Property for n=12 by introducing coloopless zonotopes.
The lonely runner conjecture holds for eight runners
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
representative citing papers
A computer-assisted proof establishes the Lonely Runner Conjecture for k=10, 11, and 12 using refined sieving and a polynomial method for specific congruence classes.
Introduces the mixed lonely runner property MLPS_k and exactly characterizes MLPS_2 while deriving Fourier-based summation and integral formulas for unequal thresholds.
Computer-assisted proofs of the Lonely Runner Conjecture are given for nine and ten runners via a refined sieve approach.
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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Eleven, twelve, and thirteen lonely runners
A computer-assisted proof establishes the Lonely Runner Conjecture for k=10, 11, and 12 using refined sieving and a polynomial method for specific congruence classes.
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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.