Download PDFOpen PDF in browserTowards Computer-Assisted Proofs of Parametric Andrews-Curtis Simplifications, IIEasyChair Preprint 133206 pages•Date: May 16, 2024AbstractWe 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
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