The Classification of Homogeneous Finite-Dimensional Permutation Structures - Braunfeld, Samuel; Simon, Pierre (The Electronic Journal of Combinatorics, 2020)
We classify the homogeneous finite-dimensional permutation structures, i.e. homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification conjectured by the first author. The primitive case was proven by the second author using model-theoretic methods, and those methods continue to appear here.