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Retracts and the Fixed Point Problem for Finite Partially Ordered Sets

Published online by Cambridge University Press:  20 November 2018

Dwight Duffus ,
Werner Poguntke  and
Ivan Rival
Dwight Duffus
Affiliation:
Department of Mathematics and Statistics the University of Calgary Calgary, AlbertaT2N 1N4
Werner Poguntke
Affiliation:
Department of Mathematics and Statistics the University of Calgary Calgary, AlbertaT2N 1N4
Ivan Rival
Affiliation:
Technische Hochschule Darmstadt Sarmstadt, Federal Republic of Germany
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A partially ordered set P has the fixed point property if every orderpreserving mapping f of P to P has a fixed point, that is, f(a) = a for some aϵP; call P fixed point free if P does not have the fixed point property.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 231 - 236
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Baclawski, K. and Björner, A., Fixed points in partially ordered sets, Advances in Math. 31 (1979) 263-287.Google Scholar
2. Birkhoff, G., Generalized arithmetic, Duke Math. J. 3 (1937), 283-302.Google Scholar
3. Davis, A. C., A characterization of complete lattices, Pacifie J. Math. 5 (1955), 311-319.Google Scholar
4. Duffus, D. and Rival, I., Crowns in dismantlable partially ordered sets, Combinatorics (Proc. Colloq. Kesthely, 1976), Colloq. Math. Jănos Bolyai 18 (1976) 271-292.Google Scholar
5. Duffus, D. and Rival, I., Retracts of partially ordered sets, J. Australian Math. Soc. (to appear).Google Scholar
6. Duffus, D., Rival, I., and Simonovits, M., Spanning retracts of a partially ordered set, Research Paper No. 396, May, 1978.Google Scholar
7. Höft, H. and Höft, M., Some fixed point theorems for partially ordered sets, Canad. J. Math. 28 (1976), 992-997.Google Scholar
8. Rival, I., A fixed point theorem for finite partially ordered sets, J. Comb. Th. 21 (1976), 309-318.Google Scholar
9. Tarski, A., A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285-309.Google Scholar