About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets |
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Authors: | Konrad Engel Nikolaj Nikolajevič Kuzjurin |
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Affiliation: | 1. Sektion Mathematik. Wilhelm-Pieck-Universit?t, 2500, Rostock, German Democratic Republic
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Abstract: | LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let . The numbers and as well as all partially ordered sets for which these maxima are attained are determined. |
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Keywords: | 06 A 10 05 A 99 |
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