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Two conjectures of Demetrovics, Füredi, and Katona, concerning partitions

✍ Scribed by Bernhard Ganter; Hans-Dietrich O.F. Gronau

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
414 KB
Volume
88
Category
Article
ISSN
0012-365X

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✦ Synopsis

It is possible to find II partitions of an n-element set whose pairwise intersections are just all atoms of the partition lattice? Demetrovics, Ftiredi and Katona verified this for all n -1 or 4 (mod 12) by constructing a series of special Mendelsohn Triple Systems. They conjectured that such triple systems exist for all n -1 (mod 3) and that the problem on the partitions has a solution for all n 3 7. We prove that both conjectures are ture, except for finitely many n.

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