On a certain class of cyclically presented groups

Edjvet, Martin; Spanu, Bruno

doi:10.1016/j.jalgebra.2011.07.020

Cited by 2 publications

(1 citation statement)

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“…Determining if a balanced presentation actually represents the trivial group (and is therefore a potential counterexample) is a nontrivial task [Edjvet et al 2001;Miasnikov and Myasnikov 2003] in its own right. A regularly-updated collection of balanced presentations arising from computational and algebraic investigations into irreducible cyclicly presented groups performed since 2001 [Edjvet 2003;Edjvet and Spanu 2011;Cremona and Edjvet 2010;Edjvet and Swan 2014] is maintained at [Edjvet 2013]. These fall into two categories:…”

Section: Problem Instancesmentioning

confidence: 99%

Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture

Krawiec,

Swan

2016

Preprint

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Motivated by the search for a counterexample to the Poincaré conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small potential counterexamples are not so numerous, and previous work has attempted to eliminate some via combinatorial search. Progress has however been limited, with the most successful approach (breadth-first-search using secondary storage) being neither scalable nor heuristically-informed. A previous empirical analysis of problem structure examined several heuristic measures of search progress and determined that none of them provided any useful guidance for search. In this article, we induce new quality measures directly from the problem structure and combine them to produce a more effective search driver via ensemble machine learning. By this means, we eliminate 19 potential counterexamples, the status of which had been unknown for some years.

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