On the average rank of LYM-sets

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

doi:10.1016/0012-365X(94)00282-N

On the average rank of LYM-sets

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

Discrete Mathematics and Mathematical Programming

Research output: Contribution to journal › Article › Academic › peer-review

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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.

Original language	English
Pages (from-to)	11-22
Number of pages	12
Journal	Discrete mathematics
Volume	95
Issue number	144
DOIs	https://doi.org/10.1016/0012-365X(94)00282-N
Publication status	Published - 1995

Keywords

METIS-140703
IR-30064

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10.1016/0012-365X(94)00282-N

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title = "On the average rank of LYM-sets",

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.",

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author = "P.L. Erdos and Erd{\"o}s, {P{\'e}ter L.} and U. Faigle and Walter Kern",

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T1 - On the average rank of LYM-sets

AU - Erdos, P.L.

AU - Erdös, Péter L.

AU - Faigle, U.

AU - Kern, Walter

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

KW - METIS-140703

KW - IR-30064

U2 - 10.1016/0012-365X(94)00282-N

DO - 10.1016/0012-365X(94)00282-N

M3 - Article

VL - 95

SP - 11

EP - 22

JO - Discrete mathematics

JF - Discrete mathematics

SN - 0012-365X

IS - 144

ER -