О Множествах Точек На Плоскости С Целочисленными Расстояниями

Avdeev, N. N.; Семенов, Э. М.

doi:10.4213/mzm11235

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2019

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“…(See [7, Exercise 2.6] for some remarks.) The constant was improved in [8] to 1/8 for all n and in [3] to 3/8 for sufficiently large n.…”

Section: Introductionmentioning

confidence: 99%

On existence of integral point sets and their diameter bounds

Avdeev

2019

Preprint

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A point set M in m-dimensional Euclidean space is called an integral point set if all the distances between the elements of M are integers, and M is not situated on an (m − 1)-dimensional hyperplane. We improve the linear lower bound for diameter of planar integral point sets. This improvement takes into account some results related to the Point Packing in a Square problem. Then for arbitrary integers m ≥ 2, n ≥ m + 1, d ≥ 1 we give a construction of an integral point set M of n points in m-dimensional Euclidean space, where M contains points M 1 and M 2 such that distance between M 1 and M 2 is exactly d.

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“…(See [7, Exercise 2.6] for some remarks.) The constant was improved in [8] to 1/8 for all n and in [3] to 3/8 for sufficiently large n.…”

Section: Introductionmentioning

confidence: 99%