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Size of the Largest Antichain in a Partition Poset

โœ Scribed by V. M. Blinovsky; L. H. Harper


Book ID
110413760
Publisher
SP MAIK Nauka/Interperiodica
Year
2002
Tongue
English
Weight
122 KB
Volume
38
Category
Article
ISSN
0032-9460

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The Size of the Largest Antichain in the
โœ E.Rodney Canfield ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 268 KB

Consider the poset 6 n of partitions of an n-element set, ordered by refinement. The sizes of the various ranks within this poset are the Stirling numbers of the second kind. Let a= 1 2 &e log(2)ร‚4. We prove the following upper bound for the ratio of the size of the largest antichain to the size of