Excluding a complete (k+1)-tuple incidence pattern on s points yields a strict o(n^{(3k+1)/(2k+1)}) upper bound on incidences between n points and n k-intersecting curves, extending Solymosi's theorem to pseudo-segments.
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Extremal structure in dense arrangements of $k$-intersecting curves
Excluding a complete (k+1)-tuple incidence pattern on s points yields a strict o(n^{(3k+1)/(2k+1)}) upper bound on incidences between n points and n k-intersecting curves, extending Solymosi's theorem to pseudo-segments.