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Séminaire Lotharingien de Combinatoire, 78B.22 (2017), 12 pp.

# Dario De Stavola

# A Plancherel Measure Associated to Set Partitions and Its Limit

**Abstract.**
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
asymptotic 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.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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