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Sharpening the LYM inequality |
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| Authors: | Péter L Erd?s P Frankl D J Kleitman M E Saks L A Székely |
| Institution: | (1) Mathematical Institute of the Hungarian Academy of Sciences, Budapest;(2) Institute of Operations Research, University of Bonn, Bonn, Germany;(3) Massachusetts Institute of Technology, 02139 Cambridge, MA, U.S.A.;(4) Eötvös University, Budapest;(5) University of New Mexico, Albuquerque;(6) University of Paris VII, 2 Place Jussieu, 75005 Paris, France;(7) University of California, San Diego |
| Abstract: | 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.Research supported in part by Alexander v. Humboldt-StiftungResearch supported in part by NSF under grant DMS-86-06225 and AFOSR grant OSR-86-0078Research supported in part by NSF grant CCR-8911388Research supported in part by OTKA 327 0113 |
| Keywords: | 05 D 05 |
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