Expected number of inversions after a sequence of random adjacent transpositions—An exact expression

Expected number of inversions after a sequence of random adjacent transpositions - An exact expression

A formula for calculating the expected number of inversions after t random adjacent transpositions has been presented by Eriksson et al. We have improved their result by determining a formula for the unknown integer sequence dr that was used in their formula and also made the formula valid for large t.

Expected number of inversions after a sequence of random adjacent transpositions

Abstract. 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, w...

The expected number of inversions after n adjacent transpositions

We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group Sm+1. We then derive from this expression the asymptotic behaviour of this number when n ≡ nm scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane.

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials