English

Symmetric functions and the explicit moment problem for abelian groups

Combinatorics 2026-01-14 v2 Number Theory Probability

Abstract

Recently, Sawin and Wood (arXiv:math/2210.06279) proved a formula for the distribution of a random abelian group GG in terms of its HH-moments E[#Sur(G,H)]\mathbb{E} [\#\operatorname{Sur}(G,H)]. We show that properties of Macdonald polynomials yield an alternate proof.

Keywords

Cite

@article{arxiv.2402.16625,
  title  = {Symmetric functions and the explicit moment problem for abelian groups},
  author = {Roger Van Peski},
  journal= {arXiv preprint arXiv:2402.16625},
  year   = {2026}
}

Comments

v1: 12 pages. First version, comments welcome! v2: minor updates in response to referee comments. Published version, appears in Proc. AMS

R2 v1 2026-06-28T15:00:24.220Z