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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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  • $\begingroup$ I'm afraid the question -- as asked -- doesn't make sense to me. Could you explain what the words mean? $\endgroup$ May 11 '11 at 14:00
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    $\begingroup$ Incomprehensible AND probably homework. Voting to close. $\endgroup$
    – Igor Rivin
    May 11 '11 at 14:19
  • $\begingroup$ 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). $\endgroup$
    – algori
    May 20 '11 at 4:47
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I searched for the meanings of the words using Google, and I suspect that this document answers your question:

www.stat.wisc.edu/~callan/notes/donaghey_bij/donaghey_bij.pdf

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