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Title of article :
The fractional dimension of subsets of Boolean lattices and of cartesian products Original Research Article
Author/Authors :
Utz Leimich، نويسنده , , Klaus Reuter، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1999
Pages :
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Abstract :
The fractional dimension of an ordered set was introduced in Brightwell and Scheinerman (1992). It is an interesting variant of the well studied order dimension and can be considered as a special case of the fractional covering number of hypergraphs. In this paper we provide a geometric interpretation of the fractional dimension and prove three theorems: The fractional dimension of the j and k-level (j < k) of a Boolean lattice is k − j + 2. Second, we deliver a formula for the product of standard orders, and third, we show that the fractional dimension is closed under Dedekind-MacNeille completion. In an appendix the fractional dimensions of 3-irreducible orders are listed.
Journal title :
Discrete Mathematics
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Link To Document :