Let pen) denote the number of different equivalence
Chapter 8, Problem 8.5.68(choose chapter or problem)
Let pen) denote the number of different equivalence relations on a set with n elements (and by Theorem 2 the number of partitions of a set with n elements). Show that p( n) satisfies the recurrence relation p( n) = L:6 C(n - I , j)p(n - j - I) and the initial condition p(O) = I. (Note: The numbers p(n) are called Bell numbers after the American mathematician E. T. Bell.)
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