Unfair permutations

Authors:
Helmut Prodinger;Carsten Schneider;Stephan Wagner
Affiliations:
Department of Mathematical Sciences, Stellenbosch University, 7602 Stellenbosch, South Africa;Research Institute for Symbolic Computation, Johannes Kepler University Linz, A-4040 Linz, Austria;Department of Mathematical Sciences, Stellenbosch University, 7602 Stellenbosch, South Africa
Venue:
European Journal of Combinatorics
Year:
2011

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Abstract

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.