Proof of Grünbaum's conjecture on the stretchability of certain arrangements of pseudolines

AbstractWe prove Grünbaum's conjecture that every arrangement of eight pseudolines in the projective plane is stretchable, i.e., determines a cell complex isomorphic to one determined by an arrangement of lines. The proof uses our previous results on ordered duality in the projective plane and on periodic sequences of permutations of [1,n] associated to arrangements of n lines in the euclidean plane