If * is a 2 k partition (a partition of 2k elements into k blocks of 2

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If ϒ* is a 2 k partition (a partition of 2k elements into k blocks of 2 elements each), show that the number of 2 k partitions ϒ satisfying ϒ ⋁ ϒ* = 1, is 2 k−1

(k −

1)!.

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