Mallows model under the Ulam distance : a feasible combinatorial approach

The Mallows model is one of the best-known probability models for permutation spaces. It is traditionally used under the Kendall’s-τ distance although it has been proposed with different distances for permutations. In this paper, we deal with the Mallows model under the Ulam distance. We show how to efficiently compute the normalization constant and the expected distance. Moreover, we propose two different sampling algorithms.