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A note on complete partitions in boolean algebras

✍ Scribed by Wojciech Sachwanowicz


Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
203 KB
Volume
36
Category
Article
ISSN
0044-3050

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We show that for every uncountable regular K and every K-complete Boolean algebra B of density 5 K there is a filter F B such that the number of partitions of length < K modulo F is 5 2'". We apply this to Boolean algebras of the form P ( X ) / I , where I is a n-complete K-dense ideal on X .

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Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2 d sets forming a d-dimensional Boolean algebra. We review extremal results for each of these classes and derive new ones for Bool

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I ) The second author's contribution to the paper comes out of his Ph. D. dissertation written 21' under the supervision of Prof. TAKEUTI to whom the author is grateful. Math. (2) 94 (1971), 201 -245.

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We give a simple proof that the number of graphical partitions of an even positive integer \(n\) is at least \(p(n)-p(n-1) . \quad 1995\) Academic Press. Inc.