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 i th 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.