Expected number of inversions after a sequence of random adjacent transpositions

Details Expected number of inversions after a sequence of random adjacent transpositions Expected number of inversions after a sequence of random adjacent transpositions

2004-11-09

arxiv.org/abs/math/0411197v1

Springer Lecture Notes special volume for FPSAC 2000, pages 677-685

Mathematics

Combinatorics

10 pages, presented at FPSAC 2000

Scientific paper

In the evolution of a genome, the gene sequence is sometimes rearranged, for example by transposition of two adjacent gene blocks. In biocombinatorics, one tries to reconstruct these rearrangement incidents from the resulting permutation. It seems that the algorithms used are too effective and find a shorter path than the real one. For the simplified case of adjacent transpositions, we give expressions for the expected number of inversions after t random moves. This average can be much smaller than t, a fact that has largely been neglected so far.

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