On combinatorics of plus–one generated line arrangements

Abstract This paper focuses on the combinatorial properties of plus–one generated line arrangements. We provide combinatorial constraints on such arrangements and construct a polynomial with a shape similar to the well–known Poincaré polynomial that decodes the plus–one generatedness property. We demonstrate how to create new plus–one generated arrangements using classical Klein and Wiman reflection arrangements. Furthermore, among all known sporadic simplicial arrangements with up to 27 lines, we identify nine minimal plus–one generated arrangements.