Abstract
We establish a general bijective framework for encoding faces of some classical hyperplane arrangements. Precisely, we consider hyperplane arrangements in R
whose hyperplanes are all of the form {x
−x
=s} for some i,j∈[n] and s∈Z. Such an arrangement A is strongly transitive if it satisfies the following condition: if {x
−x
=s}∉A and {x
−x
=t}∉A for some i,j,k∈[n] and s,t≥0, then {x
−x
=s+t}∉A. For any strongly transitive arrangement A, we establish a bijection between the faces of A and some set of decorated plane trees.