We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matoušek, and Sharir, on the sum of squares of cell complexities in such an arrangement.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics