Cohen Lenstra Partitions and Mutually Annihilating Matrices over a Finite Field

TL;DR

This paper provides a new derivation of generating functions for counting mutually annihilating matrices over finite fields, using properties of random partitions under the Cohen-Lenstra measure, motivated by algebraic geometry questions.

Contribution

It offers a novel approach to deriving counting formulas for mutually annihilating matrices via Cohen-Lenstra measure properties, differing from previous methods.

Findings

Derived generating functions for mutually annihilating matrices over finite fields.

Connected algebraic geometry questions with Cohen-Lenstra partition statistics.

Provided alternative proof techniques for matrix enumeration problems.

Abstract

Motivated by questions in algebraic geometry, Yifeng Huang recently derived generating functions for counting mutually annihilating matrices and mutually annihilating nilpotent matrices over a finite field. We give a different derivation of his results using statistical properties of random partitions chosen from the Cohen-Lenstra measure.