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Digraphs and the semigroup of all functions on a finite set

Published online by Cambridge University Press:  18 May 2009

Peter M. Higgins
Peter M. Higgins
Affiliation:
Deakin University, Victoria 3217, Australia
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Let Tn denote the full transformation semigroup on the finite set = {1, 2, … n}, that is the set of all mappings from to , with function composition as the semigroup operation. In this paper algorithms are introduced to solve equations such as axmb = c and ax = xb (a, b, c ∊ Tn), which employ a representation of members of Tn as special directed graphs.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 41 - 57
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, (Math. Surveys of the Amer. Math. Soc.7, Vol. I, Providence R.I., 1961).Google Scholar
2.Harary, F., Graph theory (Addison-Wesley, 1969).CrossRefGoogle Scholar
3.Higgins, P. M., A method for constructing square roots in finite full transformation semigroups, Bull. Canad. Math. Soc. 29 (1986), 344–351.CrossRefGoogle Scholar
4.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
5.Howie, J. M., Idempotent generators in finite full transformation semigroups, Proc. Roy. Soc. Edinburgh, Sect. A 81 (1978), 317–323.CrossRefGoogle Scholar
6.Snowden, M. and Howie, J. M., Square roots in finite full transformation semigroups, Glasgow Math. J. 23 (1982), 137–149.CrossRefGoogle Scholar