Quadrilaterals and pentagons in arrangements of lines (Q1822051)

Zusammenfassung des Autors: ''Let \(p_ k\) denote the number of k-sided faces in an arrangement of \(n\geq 5\) lines in the real projective plane. B. Grünbaum has shown that \(p_ 4\leq 1/2 n(n-3)\) and has conjectured that equality can occur only for simple arrangements. We prove this conjecture here. We also show that \(4p_ 4+5p_ 5\geq 3n\) holds for every simple arrangement of \(n\geq 4\) lines. This latter result is a strengthening of a theorem of T. O. Strommer.'' Unter anderem wird die vorhergehende Arbeit des Verf. [Discrete Math. 60, 243-251 (1986; Zbl 0608.51003)] zitiert.