# Modern books about orders and algebras on trees [closed]

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.

-

## closed as too broad by YCor, Stefan Kohl, Myshkin, Ryan Budney, Johannes HahnNov 11 '15 at 18:27

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

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? – Pete L. Clark Feb 3 '11 at 18:28
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. – Leonid Dworzanski Feb 3 '11 at 21:52
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 – Gerhard Paseman Feb 3 '11 at 21:54
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 – Gerhard Paseman Feb 3 '11 at 21:57
Perhaps the OP is talking about the "Hopf algebra of trees" in the following sense: loic.foissy.free.fr/pageperso/preprint3.pdf – Sam Hopkins Nov 7 '15 at 21:43

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

-