Homogeneity in finite ordered sets |
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Authors: | Gerhard Behrendt |
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Institution: | (1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen 1, Germany |
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Abstract: | A tower in an ordered set (X, ) is defined to be a subsetS ofX which has the property that for everysS there is a maximal chainC in {xX|xs} which is wholly contained inS. An ordered set (X, ) is called tower-homogeneous if every order isomorphism between towers in (X, ) can be extended to an automorphism of (X, ). It is shown that a finite ordered set is tower-homogeneous if and only if it can be built up from singletons stepwise by constructions of three different types. |
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Keywords: | Primary 06A06 secondary 20B25 |
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