Unfair permutations

We study unfair permutations, which are generated by letting n players draw numbers and assuming that player i draws i times from the unit interval and records her largest value. This model is natural in the context of partitions: the score of the ith player corresponds to the multiplicity of the summand i in a random partition, with the roles of minimum and maximum interchanged. We study the distribution of several parameters, namely the position of player i, the number of inversions, and the number of ascents. To perform some of the heavy computations, we use the computer algebra package Sigma.