English

On the Forking Path Conjecture

Representation Theory 2023-08-08 v2 Combinatorics

Abstract

We prove the Forking Path Conjecture for all but one element in the symmetric group S4S_4. Two specific paths in the rex graph of that element give a counterexample for the conjecture. We propose a refined conjecture for the longest element of any SnS_n.

Keywords

Cite

@article{arxiv.2307.05835,
  title  = {On the Forking Path Conjecture},
  author = {Gonzalo Jiménez},
  journal= {arXiv preprint arXiv:2307.05835},
  year   = {2023}
}

Comments

22 pages, 25 figures

R2 v1 2026-06-28T11:27:59.868Z