Geodesic
A Plancherel Measure Associated to Set Partitions and Its Limit
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@article{SLC_2017_78B_a21,
     author = {Dario De Stavola},
     title = {A {Plancherel} {Measure} {Associated} to {Set} {Partitions} and {Its} {Limit}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a21/}
}
TY  - JOUR
AU  - Dario De Stavola
TI  - A Plancherel Measure Associated to Set Partitions and Its Limit
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a21/
ID  - SLC_2017_78B_a21
ER  - 
%0 Journal Article
%A Dario De Stavola
%T A Plancherel Measure Associated to Set Partitions and Its Limit
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a21/
%F SLC_2017_78B_a21
Dario De Stavola. A Plancherel Measure Associated to Set Partitions and Its Limit. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a21/