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

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

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 retra...

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Veröffentlicht in:Order (Dordrecht) 2020-04, Vol.37 (1), p.173-178
1. Verfasser: Schröder, Bernd S. W.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Polynomials
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Zusammenfassung: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.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-019-09498-z