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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

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Embedding Euclidean buildings into products of trees

Question: Is it true that every (finite rank) Euclidean building has a biLipschitz embedding into a finite product of metric $\mathbb{R}$-trees? … , $$ C^{-1}d_X(x,y)^p \leq d_T(f(x),f(y)) \leq Cd_X(x,y)^p.$$ So what I am asking is if there is any obstruction to taking $p=1$ (maybe increasing the number of trees in the product if necessary). …
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