Hall-Littlewood polynomials and Cohen-Lenstra heuristics for Jacobians of random graphs

2014/03/03 by Jason Fulman, Fulman, Jason
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1403.0473

10 pages

arxiv created 2014/03/03 · arxiv updated 2014/03/04

Abstract

Cohen-Lenstra heuristics for Jacobians of random graphs give rise to random partitions. We connect these random partitions to the Hall-Littlewood polynomials of symmetric function theory, and use this connection to give combinatorial proofs of properties of these random partitions. In addition, we use Markov chains to give an algorithm for generating these partitions.

Related

• Probabilistic measures and algorithms arising from the Macdonald symmetric functions
• Random planar trees and the Jacobian conjecture
• Jack polynomials and some identities for partitions
• Hall-Littlewood polynomials, boundaries, and p-adic random matrices
• Symmetric functions and random partitions