Todd-Coxeter methods for inverse monoids
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Let P be the inverse monoid presentation (X|U) for the inverse monoid M, let π be the set of generators for a right congruence on M and let u Є M. Using the work of J. Stephen , the current work demonstrates a coset enumeration technique for the R-class Rᵤ similar to the coset enumeration algorithm developed by J. A. Todd and H. S. M. Coxeter for groups. Furthermore it is demonstrated how to test whether Rᵤ = Rᵥ, for u, v Є M and so a technique for enumerating inverse monoids is described. This technique is generalised to enumerate the H-classes of M. The algorithms have been implemented in GAP 3.4.4 , and have been used to analyse some examples given in Chapter 6. The thesis concludes by a related discussion of normal forms and automaticity of free inverse semigroups.
Thesis, PhD Doctor of Philosophy
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