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Jan 19, 2010 at 5:00 comment added Steve Huntsman To compress the list, save the adjacency matrix of the induced generalized de Bruijn graph and a number indicating which of the members of the generalized equivalence class it corresponds to. I have some notes from 2003 on this in the context of Kolmogorov complexity and its applications to phylogenetic analysis using mitochondrial DNA if you're interested.
Jan 18, 2010 at 22:04 comment added Rob Grey You have an interesting problem, I will think about it.
Jan 18, 2010 at 22:04 comment added Rob Grey Gerhard, I'm imagining very long sequences, where the cardinality of $S$ is in the hundreds to thousands. Also, I should add a note that one is allowed some short initial stretch of the permutation in $S$.
Jan 18, 2010 at 21:56 history answered Gerhard Paseman CC BY-SA 2.5