2016/12/09 by Dario De Stavola, De Stavola, Dario
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #math.CO #math.PR #math.RT
paper · pdf · doi:10.48550/arxiv.1612.03061
18 pages, 2 figures
arxiv created 2016/12/09 · openalex publication_date 2016/12/09 · arxiv updated 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent years increasing attention has been paid on the area of supercharacter theories, especially to those of the upper unitriangular group. A particular supercharacter theory, in which supercharacters are indexed by set partitions, has several interesting properties, which make it object of further study. We define a natural generalization of the Plancherel measure, called superplancherel measure, and prove a limit shape result for a random set partition according to this distribution. We also give a description of the asymptotical behavior of two set partition statistics related to the supercharacters. The study of these statistics when the set partitions are uniformly distributed has been done by Chern, Diaconis, Kane and Rhoades.