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The Andrews-Curtis Conjecture

The Andrews-Curtis conjecture posits that every balanced presentation of the trivial group can be transformed into the standard presentation by a finite sequence of elementary transformations. We have developed software to enumerate sequences of Andrews-Curtis moves (the ACME package), and used this to investigate the minimal potential counterexamples - which turns out to be unique. We have also investigated the connection between Andrews-Curtis proof sequences and proofs extracted from a Todd-Coxeter coset enumeration (using the PEACE package).

preprint: Breadth-first search and the Andrews-Curtis conjecture ....  [48K .ps.gz file]  or [14K .dvi.gz file]
preprint: Andrews-Curtis and Todd-Coxeter proof words ....  [46K .ps.gz file]  or [9K .dvi.gz file]
software: ACME source code (ANSI C) ....  [29K .tar.gz file]
manual: ACME 1.000: an Andrews-Curtis move enumerator ....  [43K .ps.gz file]  or [10K .dvi.gz file]
examples/utilites: stuff for 1st preprint .....  [20K .tar.gz file]