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? $\endgroup$– James CranchCommented May 11, 2011 at 14:00
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3$\begingroup$ Incomprehensible AND probably homework. Voting to close. $\endgroup$– Igor RivinCommented May 11, 2011 at 14:19
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$\begingroup$ 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). $\endgroup$– algoriCommented May 20, 2011 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
