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I am currently writing a mathematical article and we are considering some formulas given by a sum of terms that are "codified" (or maybe better, graphically represented) by trees (in the mathematical sense, a type of graphs; irrelevant for the question). I would like to find inspiration for the correct adjective for such formulas. My collaborator proposes "tree-wise" formulas. While this would not be so bad (the suffix -wise is often used in mathematics, also sometimes in places where it doesn't strictly belong), I think we can probably do better. What would be some possible adjectives indicating that an object is "made up by trees" that we could use in our context?

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  • Maybe make something from the Latin "arbor". Similar to when we use "chromatic" in relation to color. Searching in MathSciNet I can find papers with "arborescent" and "arboricity" in their titles. Even "arborified".
    – GEdgar
    Oct 13, 2020 at 14:24
  • In English, the word tree is used as an adjective: tree structure, for example.
    – Lambie
    Oct 13, 2020 at 15:59
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    I’m voting to close this question because it's asking for a purely mathematical usage, and belongs on the Mathematics.SE site. Nov 12, 2020 at 14:05
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    For whatever it's worth, treelike data structures are commonly called hierarchical. Nov 12, 2020 at 14:06

4 Answers 4

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"summation over a tree" or "tree-folding formulas" is what you are looking for.

In mathematics we have things like "optimization over a graph", meaning the optimization problem is defined in graph-like structures. Similarly, one can say that he is doing "summation over a tree", the reader will immediately understand the phrase. If you want an adjective, "tree-folding" is a good candidate. To fold something means to make something into a compact form by iterating over the indices of its elements in a pre-defined fashion. A "tree-folding formula" is a formula that is derived by folding trees (tree-like mathematical structures).

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I'd consider using arboreous, but I don't know if anyone uses that for math papers.

Adjective: arboreous aa(r)'bo-ree-us

  1. Inhabiting or frequenting trees

    "arboreous apes";

    • arboreal, tree-living
  2. Abounding in trees

    "an arboreous landscape";

    • arboraceous, woodsy, woody

3. Resembling a tree in form and branching structure

"arboreous coral found off the coast of Bermuda";

  • arboreal, arborescent, arboresque, arboriform, dendriform, dendroid, dendroidal, treelike, tree-shaped

See also: branchy, wooded

https://www.wordwebonline.com/search.pl?w=arboreous

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Not all usages can be specified by single words - otherwise language would be reduced to single words. I would suggest that your phrase:

can be graphically represented by trees

describes quite well what you are attempting.

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I suggest treed. The word is an adjective to be found in some dictionaries, it has sporadic use shown in Google ngram, and it has been used in mathematical articles, for example see

Canadian Journal of Mathematics

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