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.

中文翻译：

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不公平的排列。

我们研究不公平的排列，这些排列是通过让$ñ$ 玩家画数字并假设该玩家 $\mathrm{一世}$ 抽签 $\mathrm{一世}$从单位间隔开始计时，并记录她的最大值。在分区的情况下，此模型很自然：$\mathrm{一世}$玩家对应于被加数的倍数 $\mathrm{一世}$在随机分区中，最小和最大角色互换。我们研究几个参数的分布，即玩家的位置$\mathrm{一世}$，反转次数和上升次数。为了执行一些繁重的计算，我们使用计算机代数软件包Sigma。