Bounds on the cardinality of partition
Kerry M. Soileau
TL;DR
This paper investigates the bounds on the number of partitions of an infinite well-ordered set, establishing inequalities relating the cardinality of the power set and the set of all partitions.
Contribution
It provides new bounds on the cardinality of the set of partitions for infinite well-ordered sets, linking it to familiar cardinal functions.
Findings
|2^A| <= |Part(A)| <= |A^A| for infinite well-ordered A
Establishes inequalities relating power set and partition set sizes
Advances understanding of partition cardinalities in set theory
Abstract
If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics