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Spherical containment and the Minkowski dimension of partial orders

โœ Scribed by David A. Meyer


Publisher
Springer Netherlands
Year
1993
Tongue
English
Weight
698 KB
Volume
10
Category
Article
ISSN
0167-8094

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If P and Q are partial orders, then the dimension of the cartesian product P x Q does not exceed the sum of the dimensions of P and Q. There are several known sufficient conditions for this bound to be attained, on the other hand, the only known lower bound for the dimension of a cartesian product i

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This paper introduces a new concept of dimension for partially ordered sets. Dushnik and Miller in 1941 introduced the concept of dimension of a partial order P, as the minimum cardinality of a realizer, (i.e., a set of linear extensions of P whose intersection is P). Every poser has a greedy realiz