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On the dimension of partially ordered sets

1977; Elsevier BV; Volume: 22; Issue: 2 Linguagem: Inglês

10.1016/0097-3165(77)90046-2

ISSN

1096-0899

Autores

Oliver Pretzel,

Tópico(s)

Advanced Topology and Set Theory

Resumo

A generalization of the concept of dimension of a poset, the stable dimension, is introduced, and it is shown that there is a simple procedure for determining its value. No such procedure is known for the dimension itself. The main theorem shows that the stable dimension is equal to the maximum number of elements in a pair of antichains of the set, one lying above the other. The stable dimension can be used to find bounds for the dimension, including one which is an improvement on a bound given by W. T. Trotter, Jr., [Irreducible posets with large height exist,

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