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Is there any result known about counting the number of (unlabeled) ordered trees which follow a given unordered degree sequence?

Here an ordered tree is understood as a rooted tree in which the order of the subtrees is significant.

edited Mar 24 2012 at 21:04

asked Mar 19 2012 at 0:23

marc
27●4

Ordered in what sense? Gerhard "Ask Me About System Design" Paseman, 2012.03.18 – Gerhard Paseman Mar 19 2012 at 1:22

@Gerhard Paseman An ordered tree is a rooted tree in which the order of the subtrees is significant. – marc Mar 19 2012 at 1:24

And how is the degree sequence given? is it ordered as well? Or is it just a multiset? Gerhard "Ask Me About System Design" Paseman, 2012.03.18 – Gerhard Paseman Mar 19 2012 at 3:35

@Gerhard Paseman sorry for the unclear specification: The degree sequence is ordered as well – marc Mar 19 2012 at 4:10

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so would degree sequence 2,1,3,4,5,1,1,1,1,1,1,1 mean the root has two children, the one on the left is a leaf and the one on the right has two children , one with 3 leaves on it and one with 4? That would uniquely specify the tree so it must not be that. Can you give an example? – Aaron Meyerowitz Mar 19 2012 at 6:03

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Ira Gessel · Accepted Answer · 2012-03-19 20:37:55Z UTC

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Is Theorem 6.4 of http://people.brandeis.edu/~gessel/homepage/papers/enum.pdf what you want?

answered Mar 19 2012 at 20:37

Ira Gessel
2,359●5●15

GH · Answer 2 · 2012-03-19 04:36:44Z UTC

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See Theorem 4.3 on page 12 here.

answered Mar 19 2012 at 4:36

GH
15.1k●1●33●55

@GH Thank you for your answer. But this formula counts the number of labeled trees, whereas ordered trees are considered unlabeled. – marc Mar 19 2012 at 4:57

Number of Ordered Trees of given degree sequence

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