Permutation groups and Prufer codes

The last week was a bit hectic. It was the first time I had even been on a 13 hour flight.

I had implemented Prufer codes before I left, which is basically a one-to-one mapping to labelled trees. Using Prufer codes, we can generate trees in an ordered manner, rank and unrank them and do all sorts of other cool stuff. By placing some restrictions on the enumerated Prufer codes, we can get the number of spanning trees of a complete bipartite graph. Apart from Prufer codes, I was also fixing up the algorithms I had implemented for bracelets, fixed-density and fixed-content necklaces, Lyndon brackets (these form the basis for free Lie algebra), meanders and stamp foldings. These are really specialized routines but it was decided in the mailing list that it would be really helpful for others to read.

Once I get the Permutations branch in, I can begin work on the Permutation Groups module, so that will be my immediate task.

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