Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is shown that every homogeneous set of n points in d-dimensional Euclidean space determines at least \(\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)\) distinct distances for a constant c(d) > 0. In three-space the above general bound is slightly improved and it is shown that every homogeneous set of n points determines at least \(\Omega(n^{0.6091})\) distinct distances.
['József Solymosi', 'Csaba D. Tóth']
I am writing a research paper on a idea Distinct Distances in Homogeneous Sets in Euclidean Space
[{"from": "human", "value": "I am writing a research paper on a idea Distinct Distances in Homogeneous Sets in Euclidean Space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is shown that every homogeneous set of n points in d-dimensional Euclidean space determines at least \\(\\Omega(n^{2d/(d^2+1)} / \\log^{c(d)} n)\\) distinct distances for a constant c(d) > 0. In three-space the above general bound is slightly improved and it is shown that every homogeneous set of n points determines at least \\(\\Omega(n^{0.6091})\\) distinct distances."}]