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 language | English |
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Pages (from-to) | 11-22 |
Number of pages | 12 |
Journal | Discrete mathematics |
Volume | 95 |
Issue number | 144 |
DOIs | |
Publication status | Published - 1995 |
Keywords
- METIS-140703
- IR-30064