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Please help to find books about orders and algebras on trees. If there is no modern books, please advice good old ones! I'm more interested in finite trees (my current problem), but infinite ones are very appreciated too (as probably there is no difference between fin/inf in some contexts).

I'm especially interested in the ordered group on trees.

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    $\begingroup$ Well, from my question you can see that I won't be able to supply the references you want, but: what do you mean by an order, algebra or ordered group on a tree? $\endgroup$
    – Pete L. Clark
    Commented Feb 3, 2011 at 18:28
  • $\begingroup$ There is a way to define order on trees like: The tree $a \in \mathbb{T}$ is less than the tree $b \in \mathbb{T}$ if there is the injection $j:N \rightarrow N$ between their nodes which preserves incidence relation. ($\mathbb{T}$ - universum of trees, $N$ - set of nodes). And there is a way to define operation $+:\mathbb{T}\times\mathbb{T}\rightarrow\mathbb{T}$ as if we consider trees as multisets of multisets of $\dots$ of leaves. But this operation isn't a group operation. So I'm looking for books about such relations, operations etc. $\endgroup$
    – Leonid Dworzanski
    Commented Feb 3, 2011 at 21:52
  • $\begingroup$ I doubt that you will find exactly the book you want. You might start with conference proceedings on Algebras and Orders. Someone who might have some good pointers for you is J. D. Farley. Gerhard "Ask Me About System Design" Paseman, 2011.02.03 $\endgroup$
    – Gerhard Paseman
    Commented Feb 3, 2011 at 21:54
  • $\begingroup$ Also, I used trees to model terms in a language. You might consider asking in Theoretical Computer Science forums for some examples of literature. Gerhard "Ask Me About System Design" Paseman, 2011.02.03 $\endgroup$
    – Gerhard Paseman
    Commented Feb 3, 2011 at 21:57
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    $\begingroup$ Perhaps the OP is talking about the "Hopf algebra of trees" in the following sense: loic.foissy.free.fr/pageperso/preprint3.pdf $\endgroup$
    – Sam Hopkins
    Commented Nov 7, 2015 at 21:43

1 Answer 1

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1) Trees (Springer Monographs in Mathematics) 1st ed. 1980. Corr. 2nd printing 2002 Edition by Jean-Pierre Serre

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