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Retracts of partially ordered sets

Published online by Cambridge University Press:  09 April 2009

Dwight Duffus
Affiliation:
The University of Calgary Calgary, Canada
Ivan Rival
Affiliation:
The University of Calgary Calgary, Canada
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Abstract

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Let P be a finite, connected partially ordered set containing no crowns and let Q be a subset of P. Then the following conditions are equivalent: (1) Q is a retract of P; (2) Q is the set of fixed points of an order-preserving mapping of P to P; (3) Q is obtained from P by dismantling by irreducibles.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

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Duffus, D., Poguntke, W. and Rival, I. (1977), ‘Retracts and the fixed point problem for finite partially ordered sets’, Canad. Math. Bull. (to appear).Google Scholar
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