Assouad type dimensions for self-affine sponges with a weak coordinate ordering condition (Q1731792)

Summary: Recently self-affine sponges have been shown to be interesting counter-examples to several previously open problems. One class of recently studied sponges are \textit{Bedford-McMullen sponges with a weak coordinate ordering condition}, that is, sponges with several coordinates having the same contraction ratio. The Assouad type dimensions of such sets cannot be calculated using the same formula as the regular Bedford-McMullen sponges. We calculate the Assouad type dimensions for such sponges and the more general Lalley-Gatzouras sponges with a weak coordinate ordering condition, discussing some of their more subtle details along the way.