Again, a question closely related to a characterization of standard atoms (not to be confused with standard alphabets:). The question is a refinement of a question posted in Automorphisms vs color-preserving automorphisms in Fraisse classes, which has been answered negatively (see the recent post The colored open question closed).
We study the relationship between standard alphabets over the equality atoms, and those which can be made homogeneous using finitely many relations and functions. We leave open the problem whether these notions coincide.
This post discusses equivalence of:
1. existence of the least supports
2. representation theorem