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Fixed point property for finite ordered sets that contain no crowns with 6 or more elements. (English) Zbl 1455.06001
A poset has the fixed point property if every endomorphism has a fixed point. The problem of determining whether a finite poset has the fixed point property is co-NP-complete. This paper proves that the problem of determining whether a finite poset which omits crowns of six or more elements has the fixed point property is in P. This result is established by first proving that every finite, connected poset which omits crowns of six or more elements either has (i) an element of rank one that has a unique lower cover or (ii) a retractable minimal element.
MSC:
06A06 Partial orders, general
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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