In Sharir and Solomon (2015), Sharir and Solomon showed that the number of incidences between   m     m        distinct points and   n     n        distinct lines in   R 4        R    4          is    equation  ( 1 )     O ∗ (m 2∕5 n 4∕5 +m 1∕2 n 1∕2 q 1∕4 +m 2∕3 n 1∕3 s 1∕3 +m+n),       O    ∗        m    2  ∕  5      n    4  ∕  5    +    m    1  ∕  2      n    1  ∕  2      q    1  ∕  4    +    m    2  ∕  3      n    1  ∕  3      s    1  ∕  3    +  m  +  n    ,           provided that no 2-flat contains more than   s     s        lines, and no hyperplane or quadric contains more than   q     q        lines, where the   O ∗        O    ∗          hides a multiplicative factor of              2    c    log  m            for some absolute constant   c     c       .
['Noam Solomon', 'Ruixiang Zhang']
Highly incidental patterns on a quadratic hypersurface in R 4