# Adjective for "composed by trees" (mathematics)

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?

• 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". Oct 13, 2020 at 14:24
• In English, the word tree is used as an adjective: tree structure, for example. Oct 13, 2020 at 15:59
• 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
• For whatever it's worth, treelike data structures are commonly called hierarchical. Nov 12, 2020 at 14:06

"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).

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

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