Geodesic
Retracts and the Fixed Point Problem for Finite Partially Ordered Sets
Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 231-236

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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. 
Duffus, Dwight; Poguntke, Werner; Rival, Ivan. Retracts and the Fixed Point Problem for Finite Partially Ordered Sets. Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 231-236. doi: 10.4153/CMB-1980-031-2
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