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Give a bijective proof-----the number of oriented increasing binary trees on the vertex set $\lbrace 1,2,\cdots,n\rbrace$ is the Eulerian number $E_n$(the number of alternating permutations in $\mathfrak{S}_n$). alternating permutation is downup permutation.

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I'm afraid the question -- as asked -- doesn't make sense to me. Could you explain what the words mean? – James Cranch May 11 '11 at 14:00
Incomprehensible AND probably homework. Voting to close. – Igor Rivin May 11 '11 at 14:19
Igor -- I disagree. I think it is just incomprehensible. I've also voted to close; to be reversed if the author edits the question making it clear what they have in mind (and avoiding the imperative mood if possible). – algori May 20 '11 at 4:47

I searched for the meanings of the words using Google, and I suspect that this document answers your question:

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Thank you very much! – X--- May 11 '11 at 14:27

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