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We give a combinatorial model for the bounded derived category of gradedmodules over the dual numbers in terms of arcs on the integer line with a pointat infinity. Using this model we describe the lattice of thick subcategories ofthe bounded derived category, and of the perfect complexes, in terms ofnon-crossing partitions. We also make some comments on the symmetries of theselattices, exceptional collections, and the analogous problem for the unboundedderived category.

On the graded dual numbers, arcs, and non-crossing partitions of the integers