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We study the combinatorics of pseudoline arrangements in the real projectiveplane. Our focus lies on two classes of arrangements: simplicial arrangementsand arrangements whose characteristic polynomials have only real roots. Wederive inequalities involving the $t$-vectors of the arrangements inconsideration. As application, we obtain some finiteness and classificationresults. Moreover, we are able to prove the Dirac Motzkin Conjecture for realpseudoline arrangements whose charateristic polynomials split over$\mathbb{R}$.

Combinatorics of free and simplicial line arrangements