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Partitions of large Boolean lattices

✍ Scribed by Zbigniew Lonc

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
482 KB
Volume
131
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let 2" be the ordered set obtained from the Boolean lattice 2" by deleting both the greatest and the least elements. Definef(n) to be the minimum number k such that there is a partition of 2" into k antichains of the same size except for at most one antichain of a smaller size. In the paper we examine the asymptotic behavior of f(n) and we show that c1 n < f(n) < c2n2 for some constants c1 and c2 and n sufficiently large. Moreover, we prove for all ordered sets P of size less than 5, a conjecture that for n sufficiently large there is a partition of 2" into ordered sets isomorphic to P if and only if some obvious divisibility conditions are satisfied.

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