Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  introduce the notion of k-centerpoints for any set P of n points in ℝd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2  define two variants: affine k-centerpoints, and topological k-centerpoints.  prove their equivalence in ℝ2, and conjecture that these are in fact equivalent in any dimension.  present the first non-trivial bounds for these problems in ℝd, as ll as present several conjectures related to them.
['Nabil H. Mustafa', 'Saurabh Ray', 'Mudassir Shabbir']
I am writing a research paper on a idea k-Centerpoints Conjectures for Pointsets in ℝd
[{"from": "human", "value": "I am writing a research paper on a idea k-Centerpoints Conjectures for Pointsets in \u211dd"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  introduce the notion of k-centerpoints for any set P of n points in \u211dd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2  define two variants: affine k-centerpoints, and topological k-centerpoints.  prove their equivalence in \u211d2, and conjecture that these are in fact equivalent in any dimension.  present the first non-trivial bounds for these problems in \u211dd, as ll as present several conjectures related to them."}]