On the average rank of LYM-sets

P.L. Erdos, Péter L. Erdös, U. Faigle, Walter Kern

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2 Citations (Scopus)
41 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)11-22
Number of pages12
JournalDiscrete mathematics
Volume95
Issue number144
DOIs
Publication statusPublished - 1995

Keywords

  • METIS-140703
  • IR-30064

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