Abstract
The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-𝓁 many 1s and at most m+𝓁 many 1s, i.e., the vertices in the middle 2 𝓁 levels, has a Hamilton cycle for any m >= 1 and 1 = 1 and 1 = 2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code.