Describing a Matsubara coordinate concisely is difficult due to the (usual) high dimensionality of a Matsubara space. In order to discuss individual ADOs we need to define each of the axes and positions along those axes. We can define each Matsubara dimension as an integer M {•} and the ADO position along that axis as n. From this definition we could, for example, write an ADO which is tier 3 in M 1 and tier 2 in M 5, but zero along all other axes, within an 8-dimensional Matsubara space as (3, 0, 0, 0, 2, 0, 0, 0), or more concisly as 3 1 2 5 .