MathDB

89

Part of 1990 IMO Longlists

Problems(1)

Find number of functions - ILL 1990 THA3

Source:

9/19/2010
Let nn be a positive integer. S1,S2,…,SnS_1, S_2, \ldots, S_n are pairwise non-intersecting sets, and SkS_k has exactly kk elements (k=1,2,…,n)(k = 1, 2, \ldots, n). Define S=S1∪S2∪⋯∪SnS = S_1\cup S_2\cup\cdots \cup S_n. The function f:S→Sf: S \to S maps all elements in SkS_k to a fixed element of SkS_k, k=1,2,…,nk = 1, 2, \ldots, n. Find the number of functions g:S→Sg: S \to S satisfying f(g(f(x)))=f(x).f(g(f(x))) = f(x).
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