Sharpening the LYM inequality


The level sequence of a Sperner familyF is the sequencef(F)={f i (F)}, wheref i (F) is the number ofi element sets ofF . TheLYM inequality gives a necessary condition for an integer sequence to be the level sequence of a Sperner family on ann element set. Here we present an indexed family of inequalities that sharpen theLYM inequality.

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Research supported in part by Alexander v. Humboldt-Stiftung

Research supported in part by NSF under grant DMS-86-06225 and AFOSR grant OSR-86-0078

Research supported in part by NSF grant CCR-8911388

Research supported in part by OTKA 327 0113

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Erdős, P.L., Frankl, P., Kleitman, D.J. et al. Sharpening the LYM inequality. Combinatorica 12, 287–293 (1992).

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