Erdős, Péter and Faigle, U. and Kern, W.
(1995)
*On the Average Rank of LYM-sets.*
DISCRETE MATHEMATICS, 144 (1-3).
pp. 11-22.
ISSN 0012-365X

Text
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## Abstract

Let S be a finite set with some rank function r such that the Whitney numbers w(i) = \{x is an element of S\r(x)= i}\ are log-concave. Given k, m is an element of N so that w(k-1) < w(k) less than or equal to w(k+m), set W = w(k) + w(k+1) + ... + w(k+m). Generalizing a theorem of Kleitman and Milner, we prove that every F subset of or equal to S with cardinality \F\ greater than or equal to W has average rank at least (kw(k) + ... + (k + m)w(k+m))/W, provided the normalized profile vector (x(1),...,x(n)) of F satisfies the following LYM-type inequality: x(0) + x(1) + ... + x(n) less than or equal to m + 1.

Item Type: | Article |
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Subjects: | Q Science / természettudomány > QA Mathematics / matematika |

SWORD Depositor: | MTMT SWORD |

Depositing User: | MTMT SWORD |

Date Deposited: | 06 Feb 2014 04:03 |

Last Modified: | 06 Feb 2014 04:03 |

URI: | http://real.mtak.hu/id/eprint/9924 |

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