We study substructures of a projective space
PG(
n, 2) represented in terms of elementary combinatorics of finite sets, which generalize the Sylvester’s representation of the
generalized quadrangle of order (2, 2). Their synthetic properties are established and automorphisms are characterized.
Keywords Fano projective space - Combinatorial Grassmannian - Veblen configuration - Net (configuration) - Generalized quadrangle
Mathematics Subject Classification (2000) 51A45 - 51E20
Communicated by Guglielmo Lunardon.