Unformatted text preview: following analog of Pascal’s relations: S ( n,k ) = S ( n1 ,k1) + kS ( n1 ,k ) for k,n > 0. [Hint: if X denotes the set of partitions of [ n ] into k parts, consider the decomposition X = A ∪ B , where A consists of partitions in which { n } is a block, and B consists of partitions in which n belongs to a block containing at least one other element.] Use the above relation and the initial conditions S ( n, 0) = 1 if n = 0, S ( n, 0) = 0 if n > 0 to make a table of S ( n,k ) for n and k less than or equal to 7. Check by comparing the value for S (7 , 3) in your table to the value given by the formula in Chapter 5.5....
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 Fall '08
 STRAIN
 Math, Equivalence relation, Transitive relation, smallest equivalence relation, transitive closure R∗

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