Fully-projected subsets

الأصل · EN

Let k and i₁,,iₙ be natural numbers. Place k balls into a multidimensional box of i₁× × iₙ cells, no more than one ball to each cell, such that the projections to each of the coordinate axes have cardinalities i₁,,iₙ, respectively. We generalize earlier work of Wang, Lee, and Tan to find a formula for the alternating sum of the number of these fully-projected subsets.