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On CCC boolean algebras and partial orders

András Hajnal, István Juhász, Zoltán Szentmiklóssy (1997)

Commentationes Mathematicae Universitatis Carolinae

We partially strengthen a result of Shelah from [Sh] by proving that if κ = κ ω and P is a CCC partial order with e.g. | P | κ + ω (the ω th successor of κ ) and | P | 2 κ then P is κ -linked.

On colored set partitions of type B n

David Wang (2014)

Open Mathematics

Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized and...

On completeness and direction in fuzzy relational systems.

Pedro J. Burillo López, Ramón Fuentes-González, León A. González Sotos (1998)

Mathware and Soft Computing

The concepts of bounded subset, complete subset and directed subset, wich are well known in the context of partially ordered sets (X,≤), are extended in order to become appliable, with coherence, in fuzzy relational systems (X,R). The properties of these generalized structures are analyzed and operative exemples of them are presented.

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