Annals of Combinatorics

, Volume 23, Issue 2, pp 295–315 | Cite as

Random Partitions and Cohen–Lenstra Heuristics

  • Jason FulmanEmail author
  • Nathan Kaplan


We investigate combinatorial properties of a family of probability distributions on finite abelian p-groups. This family includes several well-known distributions as specializations. These specializations have been studied in the context of Cohen–Lenstra heuristics and cokernels of families of random p-adic matrices.


Cohen–Lenstra heuristics Hall–Littlewood polynomial Probability measure Random matrices Random partitions Finite abelian group 

Mathematics Subject Classification

15B52 05E05 



Fulman is supported by Simons Foundation Grant 400528. Kaplan is supported by NSA Young Investigator Grant H98230-16-10305, NSF Grant DMS 1802281 and by an AMS-Simons Travel Grant. The authors thank the referees, Gilyoung Cheong, and Melanie Matchett Wood for helpful comments.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of CaliforniaIrvineUSA

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