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Fixed Point Property for Finite Ordered Sets that Contain No Crowns with 6 or More Elements

  • Bernd S. W. SchröderEmail author
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Abstract

We prove that, for a finite ordered set P that contains no crowns with 6 or more elements, it can be determined in polynomial time if P has the fixed point property. This result is obtained by proving that every such ordered set must contain a point of rank 1 that has a unique lower cover or a retractable minimal element.

Keywords

Ordered set Fixed point property Crown Irreducible point Retractable point d2-collapsible Dimension 2 

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Notes

Acknowledgements

The author thanks the referees for constructive suggestions that improved and streamlined the presentation.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and Natural SciencesThe University of Southern MississippiHattiesburgUSA

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