The slimmest arrangements of hyperplanes. I: Geometric lattices and projective arrangements (Q792330)

[For part II see Mathematika 28, 169-179 (1981; Zbl 0483.51012).] A projective d-arrangement of hyperplanes in real projective d-space is a finite set of hyperplanes, whose intersection is empty, and the resulting cell-complex decomposition of the space. The author is concerned with the establishment and characterization of lower bounds for the numbers of k- dimensional cells and k-dimensional flats in the d-arrangement \((0<k\leq d)\). Generalizations of Whitney numbers in a geometric lattice are used to this end.