Note: Semi-Order Dimension Two is a Comparability Invariant |
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| Authors: | Felsner Stefan Möhring Rolf H |
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| Institution: | (1) Fachbereich Mathematik, Institut für Informatik, Freie Universität Berlin, Takustraße 9, 14195 Berlin, Germany;(2) Fachbereich Mathematik, Technische Universität Berlin, MA 6-1, Straße des 17. Juni 135, Berlin, Germany |
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| Abstract: | A partial order P =(X, <
P
) is a semi-order if it is an interval order admitting an interval representation such that all the intervals are of unit length. The semi-order dimension of P is the smallest k for which there exist k semi-order extensions of P which realize P. In 1992 the question whether semi-order dimension is a comparability invariant was posed. We prove that for k = 2 this is the case. |
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| Keywords: | comparability invariance dimension partially ordered sets |
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