Comparing Gröbner bases and word reversing

Details Comparing Gröbner bases and word reversing Comparing Gröbner bases and word reversing

2007-12-04

arxiv.org/abs/0712.0525v1

Mathematics

Group Theory

Scientific paper

Gr\"obner bases, in their noncommutative version, and word reversing are methods for solving the word problem of a presented monoid, and both rely on iteratively completing the initial list of relations. Simple examples may suggest to conjecture that both completion procedures are closely related. Here we disprove this conjecture by exhibiting families of presentations for which they radically differ.

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