Towards Computer-Assisted Proofs of Parametric Andrews-Curtis Simplifications, II

EasyChair Preprint no. 13320

Abstract

We present recent developments in the applications of automated theorem proving in the investigation of the Andrews-Curtis conjecture. We demonstrate previously unknown simplifications of groups presentations from a parametric family $MS_{n}(w_{\ast})$ of trivial group presentations for $n = 3,4,5,6,7$ (subset of well-known Miller-Schupp family). Based on the human analysis of these simplifications we formulate two conjectures on the structure of simplifications for the infinite family $MS_{n}(w_{\ast})$, $n \ge 3$.

This is an extended and updated version of the abstract presented at AITP 2023 conference.

Keyphrases: Andrews-Curtis conjecture, automated reasoning, combinatorial group theory

@Booklet{EasyChair:13320,
  author = {Alexei Lisitsa},
  title = {Towards Computer-Assisted Proofs of Parametric Andrews-Curtis Simplifications, II},
  howpublished = {EasyChair Preprint no. 13320},

  year = {EasyChair, 2024}}