: Curtis' Western Indians . Ralph W. Andrews.

The Finitary Andrews-Curtis Conjecture

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexam...

On the Andrews-Curtis equivalence

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of \elementary transformations" which are Nielsen transformations augmented by arbitrary conjugations. It is a prevalent opinion that this conjecture is false; however, not many potential counterexamples are known. In this paper, we show that some of the pr...

Genetic algorithms and the Andrews-Curtis conjecture

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be transformed into the trivial presentation by a finite sequence of “elementary transformations” which are Nielsen transformations together with an arbitrary conjugation of a relator. It is believed that the Andrews-Curtis conjecture is false; however, not so many possible counterexamples are known. ...

Fitness Landscapes and the Andrews-Curtis Conjecture

JERRY SWAN1, GABRIELA OCHOA1, GRAHAM KENDALL1, MARTIN EDJVET2 1Automated Scheduling, Optimisation and Planning (ASAP) Research Group, School of Computer Science and Information Technology, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK. Tel.: (+44) (0)115 846 6504, Fax: +44 (0)115 846 7877. 2School of Mathematical Sciences, University of Nottingham, University P...

Fast Searching for Andrews-Curtis Trivializations