Proves a superlinear lower bound on the diameter of planar integral point sets in semi-general position.
On the characteristic of integral point sets in $\mathbb{E}^m$
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abstract
We generalise the definition of the characteristic of an integral triangle to integral simplices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral point sets. Using this algorithm we are able to provide new exact values for the minimum diameter of integral point sets.
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math.CO 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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On diameter bounds for planar integral point sets in semi-general position
Proves a superlinear lower bound on the diameter of planar integral point sets in semi-general position.