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Product partial orders with the sperner property

โœ Scribed by Robert A. Proctor; Michael E. Saks; Dean G. Sturtevant

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
754 KB
Volume
30
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Sufficient conditions are established for the product of two ranked partially ordered sets to have the Sperner property. As a consequence, it is shown that the class of strongly Sperner rank-unimodal rank-symmetric partially ordered sets is closed under the operation of product. Counterexamples are given which preclude most small variations in the hypotheses or cnnclusions of the two main results.

๐Ÿ“œ SIMILAR VOLUMES

Unichain coverings in partial orders wit
Unichain coverings in partial orders with the nested saturation property
โœ Douglas B. West ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 457 KB

The theory of saturated chain partitions of partial orders is applied to the minimum unichain covering problem in the product of partial orders (posets). Define the nested saturation property for a poset to be the existence of a sequence of chain partitions %,, %a, . . such that (e, is k-and k + l-s

The dimension of the Cartesian product o
The dimension of the Cartesian product of partial orders
โœ William T Trotter Jr. ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 546 KB

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