On forbidden configurations for strong posets
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The concept of strong elements in posets is introduced. Several properties of strong elements in different types of posets are studied. Strong posets are characterized in terms of forbidden structures. It is shown that many of the classical results of lattice theory can be extended to posets. In particular, we give several characterizations of strongness for upper semimodular (USM) posets of finite length. We characterize modular pairs in USM posets of finite length and we investigate the interrelationships between consistence, strongness, and the property of being balanced in USM posets of finite length. In contrast to the situation in upper semimodular lattices, we show that these three concepts do not coincide in USM posets.
Mathematics Subject Classification (2000):06B, 06C10, 06D15.
Key words:Upper semimodular posets strong posets balanced posets consistent
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