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Continuing the convention above, let pi , sigma be two partitions in Pi n . Define a relation on { 1 ,

Continuing the convention above, let \pi ,\sigma be two partitions in \Pi n. Define a relation
on {1,2,..., n} by declaring a b whenever there exists a sequence of elements
a = e0, e1,..., ek = b (k can be equal to 0) such that for each i =1,..., k, either
ei1, ei are in the same part of \pi or in the same part of \sigma (or both). Show that

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