Abstract
Given a poset (A, r) and an acyclic r-monotone function f: A→A, we prove that r can be extended to a linear order R with xRy⇛f(x)Rf(y) for all x, y∈A.
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References
E.Szpilrajn (1930) Sur l'extension de l'ordre partiel, Fund. Math. 16, 386–389.
W. T.TrotterJr. and J. I.MooreJr. (1977) The dimension of planar posets, J. Comb. Theory 22, 54–67.
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Communicated by W. T. Trotter
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Szigeti, J., Nagy, B. Linear extensions of partial orders preserving monotonicity. Order 4, 31–35 (1987). https://doi.org/10.1007/BF00346650
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DOI: https://doi.org/10.1007/BF00346650