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Idempotent depth in semigroups of order-preserving mappings

Published online by Cambridge University Press:  14 November 2011

Peter M. Higgins
Peter M. Higgins
Affiliation:
Department of Mathematics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, U.K.
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Extract

We introduce algorithms for calculating minimum length factorisations of order-preserving mappings on a finite chain into products of idempotents, and into products of idempotents of defect one. The least upper bounds for these lengths are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 1045 - 1058
Copyright
Copyright © Royal Society of Edinburgh 1994

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References

1Doyen, J.. Equipotence et unicité de systèmes generateurs minimaux dans certains monoides. Semigroup Forum 28 (1984), 341–346.CrossRefGoogle Scholar
2Gomes, G. M. S. and Howie, J. M.. On the ranks of certain semigroups of order-preserving transformations. Semigroup Forum 45 (1992), 272–282.CrossRefGoogle Scholar
3Higgins, P. M.. Techniques of Semigroup Theory (Oxford: Oxford University Press, 1992).CrossRefGoogle Scholar
4Higgins, P. M.. On a conjecture of Pin. University of Essex Mathematics Dept. Report No. 92–13.Google Scholar
5Howie, J. M.. The subsemigroup generated by the idempotents of a full transformation semigroup. J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
6Howie, J. M.. Products of idempotents in certain semigroups of transformations. Proc. R. Soc. Edinburgh Sect. A 17 (1971), 233–236.Google Scholar
7Howie, J. M.. Products of idempotents in finite full transformation semigroups. Proc. R. Soc. Edinburgh Sect. A 86 (1980), 243–254.CrossRefGoogle Scholar
8Howie, J. M. and Schein, B. M.. Products of idempotent order-preserving transformations. J. London Math. Soc. (2) 7 (1973), 357–366.CrossRefGoogle Scholar
9Iwahori, N.. A length formula in semigroups of mappings. J. Fac. Sci. Univ. Tokyo Sec. I A, Math. 24 (1977), 255–260.Google Scholar
10Pin, J. E.. Varieties of Formal Languages (London: Plenum Press, 1986).CrossRefGoogle Scholar
11Saito, T.. Products of idempotents in finite full transformation semigroups. Semigroup Forum 39 (1989), 295–309.CrossRefGoogle Scholar
12Schein, B. M.. Products of idempotent order-preserving transformations of arbitrary chains. Semigroup Forum 11 (1976), 297–309.CrossRefGoogle Scholar