Anshu, AnuragGangopadhyay, RahulShannigrahi, SaswataVusirikala, Satyanarayana2024-02-072017-02Anshu, Anurag, Rahul Gangopadhyay, Saswata Shannigrahi, Satyanarayana Vusirikala. "On the rectilinear crossing number of complete uniform hypergraphs." Computational Geometry 61 (2017): 38-47. DOI: 10.1016/j.comgeo.2016.11.0010925-7721https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37377722In this paper, we 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 in the d-dimensional rectilinear drawing of a d-uniform hypergraph is known as the d-dimensional rectilinear crossing number of the hypergraph. The currently best-known lower bound on the d-dimensional rectilinear crossing number of a complete d-uniform hypergraph with n vertices in general position in ℝd is Ω(2dd√logd)(n2d). In this paper, we improve this lower bound to Ω(2d)(n2d). We also consider the special case when all the vertices of a d-uniform hypergraph are placed on the d-dimensional moment curve. For such complete d-uniform hypergraphs with n vertices, we show that the number of pairwise crossing hyperedges is Θ(4dd√)(n2d).en-USComputational MathematicsComputational Theory and MathematicsControl and OptimizationGeometry and TopologyComputer Science ApplicationsJournal Article2024-02-0710.1016/j.comgeo.2016.11.001