A COUNTING PROBLEM OF PERSPECTIVE SIMPLEXES IN PG(n, q)

Authors

  • Debahuti Paikaray Silicon University Author
  • Susmita Biswal Silicon University Author
  • Saroj Kanta Misra Silicon University Author
  • Prayag Prasad Mishra Silicon University Author

Keywords:

Finite Projective Geometry, Perspective Tetrahedrons, Perspective Simplexes, Homogeneous Coordinates

Abstract

We start with a tetrahedron in ,  is not a power of 2, and a point  not on the faces of and found that the number of non-degenerate tetrahedrons that are perspective  with from the centre  and exclusive of the points  and s is equal to . If these tetrahedrons can have one of their vertices as  then the number of such non-degenerate tetrahedrons that are perspective with from the centre  is equal to . These propositions are proved analytically using the homogeneous coordinates of the vertices of the tetrahedrons and other counting results in finite geometries. Further, the propositions are generalised to  with cases 

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Published

2025-09-16

Issue

Vol. 43 No. 9 (2025)

Section

Articles