Inequalities in dimension theory for posets

Author:
William T. Trotter

Journal:
Proc. Amer. Math. Soc. **47** (1975), 311-316

MSC:
Primary 06A10

DOI:
https://doi.org/10.1090/S0002-9939-1975-0369192-2

MathSciNet review:
0369192

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Abstract | References | Similar Articles | Additional Information

Abstract: The dimension of a poset , denoted , is the minimum number of linear extensions of whose intersection is . It follows from Dilworth's decomposition theorem that . Hiraguchi showed that . In this paper, denotes an antichain of and the set of maximal elements. We then prove that and . We also construct examples to show that these inequalities are sharp.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0369192-2

Keywords:
Poset,
dimension,
irreducible

Article copyright:
© Copyright 1975
American Mathematical Society