The dioperad Y^{(n)} is Koszul, shown by analyzing subcomplexes of assocoipahedra via their correspondence to cloven Strebel differentials on CP^1 and deducing vanishing higher cohomology.
Meromorphic quadratic differentials and measured foliations on a Riemann surface
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Koszulity of a certain dioperad
The dioperad Y^{(n)} is Koszul, shown by analyzing subcomplexes of assocoipahedra via their correspondence to cloven Strebel differentials on CP^1 and deducing vanishing higher cohomology.