I suspect that this is not known but it can be accomplished. Further, it matters not how large is the de Bruijn sequence; all of them can be so transformed, from one de Bruijn sequence into another de Bruijn sequence in O(1) time.
It seems that mathematics and computation are difficult topics for the ResearchGate community of scholars.
OK. Thinking about tiles, all the 10 tiles having some in-key (say 21 for a 3-tile on the digits) will be found in linear order in a list of tiles; i.e., 211 follows 210, and 219 follows 218, and so the ten tiles are located together. So, tiles are easy to find; they index themselves in the list of all tiles. If we keep a second list that shows the order in which these tiles are added to the sequence, then we know the order of the tiles in the sequence, and we can use this to ensure that shuffling yields but one linked list of subsequences; i.e., one sequence. This can be done exactly one time. You build the de Bruijn sequence and keep track of the order in which tiles are added (keep two lists - for efficiency, two arrays) at the same time, and that gives sufficient information that for one time, and one time only, the de Bruijn sequence can be transformed into another de Bruijn sequence in O(1) time.
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