1997 | OriginalPaper | Chapter
A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Integers
Author : Doron Zeilberger
Published in: Advances in Combinatorial Methods and Applications to Probability and Statistics
Publisher: Birkhäuser Boston
Included in: Professional Book Archive
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Kirk (1993) raised the question of comparing the following two ways for labelling balls. Given r pre-determined positive integers n i (1 ≤ i ≤ r), and given N balls (N large), consider two ways to randomly assign r–component vectors of integers (a1,…, a r ) to them, such that 1 ≤ a i ≤ n i . We will call these vectors labels. Of course, altogether there are $$\prod {_{i = 1}^r \,n_i }$$ possible labels.