Séminaire Lotharingien de Combinatoire, 82B.55 (2019), 12 pp.

Gene B. Kim and Sangchul Lee

Modifying Curtiss' theorem to prove central limit theorems

Abstract. The distribution of descents in fixed conjugacy classes of Sn has been studied, and it is shown that its moments have interesting properties. Kim and Lee showed, by using Curtiss' theorem and moment generating functions, how to prove a central limit theorem for descents in arbitrary conjugacy classes of Sn. In this paper, we prove a modified version of Curtiss' theorem to shift the interval of convergence in a more convenient fashion and use this to show that the joint distribution of descents and major indices in conjugacy classes is asymptotically bivariate normal.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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