| Uniformly selected random permutations have been extensively analyzed in the combinatorics and probability literature. Significantly less research has been reported on permutations selected from non-uniform measures. In this thesis, we analyze various characteristics of permutations selected from the Mallows measure: a probability measure on permutations that assigns mass according to the number of inversions of the permutation. In addition, we analyze a new characteristic of the permutation, the maximum element of the inversion table which we call the level. We also develop algorithms for sampling from the Mallows measure, as well as uniformly from all permutations with a fixed number of inversions. |
