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Abstract:  We study strong exceptional collections of line bundles on Fano toric Deligne-Mumford stacks with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category of the stack, as long as the number of elements in the collection equals the rank of the (Grothendieck) K-theory group of the stack. 
The problem reduces to an interesting combinatorial problem and is solved by combinatorial means.