Random Partitions and Cohen-Lenstra Heuristics

TL;DR

This paper explores the combinatorial properties of probability distributions on finite abelian p-groups, connecting them to Cohen-Lenstra heuristics and random p-adic matrix cokernels.

Contribution

It introduces a unified framework for analyzing distributions on finite abelian p-groups, encompassing several well-known cases and their combinatorial aspects.

Findings

Identifies combinatorial structures underlying these distributions

Links distributions to Cohen-Lenstra heuristics

Provides insights into cokernels of random p-adic matrices

Abstract

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.