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This paper establishes a new lower bound on the number of unit distances between vertices of a convex polygon, proving that for every n > 4, there exists a convex n-gon with 2n - 7 unit-distance pairs. This result improves upon the previous lower bound of ⌊(5n - 5)/3⌋ by Erdős and Moser for n > 17. The construction involves a specific arrangement of points around three circles, ensuring the convexity and the required distance properties.

Author

allanzhaohm

Language

EN