Omittable lines - Berman, Leah (Ars mathematica contemporanea, 2008)
Given a collection of ?$n$? lines in the real projective plane, a line ?$\ell$? is said to be omittable if ?$\ell$? is free of ordinary points of intersection; in other words, if all the intersection points of ?$\ell$? with other lines from the collection come at the intersection of three or more lines. Given a collection of lines ?$\mathcal{L}$?, denoting by ?$\mathcal{O(L)}$? the set of all omittable lines in the collection and by ?$g(\mathcal{L})$? the cardinality of ?$\mathcal{O(L)}$?, we describe three infinite families of lines that can serve as ?$\mathcal{O(L)}$? for suitable ?$\mathcal{L}$? and also display a finite set of sporadic additional examples in which ?$\mathcal{O(L)}$? does not fall into any of the three families. We derive bounds on the size of ?$g(\mathcal{L})$? when ?$\mathcal{O(L)}$? falls into one of the three infinite families and weaker bounds for the more general case.
Keywords: geometrija; konfiguracije; matematika