Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider a generalized version of the rectilinear crossing number problem of drawing complete graphs on a plane. The minimum number of crossing pairs of hyperedges among all  d -dimensional rectilinear drawings of a  d -uniform hypergraph is known as the  d -dimensional rectilinear crossing number of the hypergraph. The currently best-known lor bound on the  d -dimensional rectilinear crossing number of a complete  d -uniform hypergraph with  n    vertices in general position in   R d        R    d          is            Ω   (     2    d     d    log  ⁡  d  )    (     n       2  d      )        . ,  improve this lor bound to            Ω  (    2    d    )   (     n       2  d      )        .  also consider the special case when all the vertices of a  d -uniform hypergraph are placed on the  d -dimensional moment curve. For such  d -dimensional rectilinear drawings of the complete  d -uniform hypergraph with  n    vertices,  show that the number of crossing pairs of hyperedges is            Θ   (     4    d     d    )    (     n       2  d      )        .
['Anurag Anshu', 'Rahul Gangopadhyay', 'Saswata Shannigrahi', 'Satyanarayana Vusirikala']
I am writing a research paper on a idea On the Rectilinear Crossing Number of Complete Uniform Hypergraphs
[{"from": "human", "value": "I am writing a research paper on a idea On the Rectilinear Crossing Number of Complete Uniform Hypergraphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider a generalized version of the rectilinear crossing number problem of drawing complete graphs on a plane. The minimum number of crossing pairs of hyperedges among all  d -dimensional rectilinear drawings of a  d -uniform hypergraph is known as the  d -dimensional rectilinear crossing number of the hypergraph. The currently best-known lor bound on the  d -dimensional rectilinear crossing number of a complete  d -uniform hypergraph with  n \u00a0  vertices in general position in   R d        R    d          is            \u03a9   (     2    d     d    log  \u2061  d  )    (     n       2  d      )        . ,  improve this lor bound to            \u03a9  (    2    d    )   (     n       2  d      )        .  also consider the special case when all the vertices of a  d -uniform hypergraph are placed on the  d -dimensional moment curve. For such  d -dimensional rectilinear drawings of the complete  d -uniform hypergraph with  n \u00a0  vertices,  show that the number of crossing pairs of hyperedges is            \u0398   (     4    d     d    )    (     n       2  d      )        ."}]