caa a22 4500 469075317 CHVBK 20180323132933.0 cr unu---uuuuu 170328e19920401xx s 000 0 eng 10.1007/BF02187848 doi (NATIONALLICENCE)springer-10.1007/BF02187848 Counting facets and incidences [Elektronische Daten] [Pankaj Agarwal, Boris Aronov] We show thatm distinct cells in an arrangement ofn planes in ℝ3 are bounded byO(m 2/3 n+n 2) faces, which in turn yields a tight bound on the maximum number of facets boundingm cells in an arrangement ofn hyperplanes in ℝ d , for everyd≥3. In addition, the method is extended to obtain tight bounds on the maximum number of faces on the boundary of all nonconvex cells in an arrangement of triangles in ℝ3. We also present a simpler proof of theO(m 2/3 n d/3+n d−1) bound on the number of incidences betweenn hyperplanes in ℝ d andm vertices of their arrangement. Springer-Verlag New York Inc., 1992 Agarwal Pankaj Computer Science Department, Duke University, 27706, Durham, NC, USA aut Aronov Boris Computer Science Department, Polytechnic University, 11201, Brooklyn, NY, USA aut Discrete & Computational Geometry Springer New York 7/4(1992-04-01), 359-369 0179-5376 7:4<359 1992 7 454 https://doi.org/10.1007/BF02187848 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02187848 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Agarwal Pankaj Computer Science Department, Duke University, 27706, Durham, NC, USA aut NATIONALLICENCE 700 1- Aronov Boris Computer Science Department, Polytechnic University, 11201, Brooklyn, NY, USA aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 7/4(1992-04-01), 359-369 0179-5376 7:4<359 1992 7 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer