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This paper proves the upper limit of mutually touching cylinders is 18, suggesting a re-evaluation of Littlewood’s conjecture.
Let N denote the maximum number of congruent infinite cylinders that can be arranged in R³ so that every pair of cylinders touches each other. Littlewood posed the question of whether $N=7$, which remains unsolved. In this paper, we prove that N≤ 18, improving the previously known upper bound of $24$ established by A. Bezdek.
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Junnosuke Koizumi (2025) studied this question.
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