English

Honeycombs for Hall polynomials

Combinatorics 2020-02-05 v2

Abstract

We propose a new formulation of Hall polynomials in terms of honeycombs, which were previously introduced in the context of the Littlewood--Richardson rule. We prove a Pieri rule and associativity for our honeycomb formula, thus showing equality with Hall polynomials. Our proofs are linear algebraic in nature, extending nontrivially the corresponding bijective results for ordinary Littlewood--Richardson coefficients [A. Knutson, T. Tao, C. Woodward, 2004].

Keywords

Cite

@article{arxiv.1909.10720,
  title  = {Honeycombs for Hall polynomials},
  author = {Paul Zinn-Justin},
  journal= {arXiv preprint arXiv:1909.10720},
  year   = {2020}
}
R2 v1 2026-06-23T11:23:54.806Z