On the average rank of LYM-sets


Erdös, Péter L. and Faigle, Ulrich and Kern, Walter (1995) On the average rank of LYM-sets. Discrete Mathematics, 144 (1-3). pp. 11-22. ISSN 0012-365X

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Abstract:Let S be a finite set with some rank function r such that the Whitney numbers wi = |{x  S|r(x) = i}| are log-concave. Given so that wk − 1 < wk wk + m, set W = wk + wk + 1 + … + wk + m. Generalizing a theorem of Kleitman and Milner, we prove that every F S with cardinality |F| W has average rank at least kwk + … + (k + m) wk + m/W, provided the normalized profile vector x1, …, xn of F satisfies the following LYM-type inequality: x0 + x1 + … + xn m + 1.
Item Type:Article
Copyright:© 1995 Elsevier Science
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/30064
Official URL:https://doi.org/10.1016/0012-365X(94)00282-N
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