Thread: Combinatorics
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Old 2006-04-21, 07:58   #1
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Dec 2005

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Default Combinatorics

You have a set of k!+k-1 elements (k>1), numbered 1, 2,..., k!+k-1 .
Let A be the set of subsets with exactly k elements.
Let B be the set of subsets with exactly k-1 elements, which includes also all the permutations of such a subset (so if for instance k=4 then the subsets {1,2,3},{1,3,2},{2,3,1},{2,1,3},{3,1,2}{3,2,1} are all in B.

Evidently #A=#B

Can you construct a bijection f such that f(A_i)=B_i and such that for all i
A_i contains B_i ?
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