A New Distribution Problem of Balls into Urns, and How to Color a Graph by Different-sized Sets
نویسنده
چکیده
Balls into urns. We have n labelled urns and an unlimited supply of balls of k different colors. Into each urn we want to put balls, no two the same color, so that the number of colors in every urn is different. Balls of the same color are indistinguishable and we don’t care if several are in an urn. How many ways are there to do this? (The reader will note the classical terminology. Our question appears to be new but it could as easily have been posed a hundred years ago.) Call the answer χ n (k). We form the exponential generating function,
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