Polynomial LYM inequalities

Christian Bey

doi:10.1007/s00493-005-0002-x

Polynomial LYM inequalities

Christian Bey^*

^*Corresponding author for this work

Institute of Mathematics

13 Citations (Scopus)

Abstract

For a Sperner family A ⊆ 2^[n] let A_i denote the family of all i-element sets in A. We sharpen the LYM inequality ∑_i |A_i|/(_iⁿ) ≤ 1 by adding to the LHS all possible products of fractions |A_i|/(_i ⁿ), with suitable coefficients. A corresponding inequality is established also for the linear lattice and the lattice of subsets of a multiset (with all elements having the same multiplicity).

Original language	English
Journal	Combinatorica
Volume	25
Issue number	1
Pages (from-to)	19-38
Number of pages	20
ISSN	0209-9683
DOIs	https://doi.org/10.1007/s00493-005-0002-x
Publication status	Published - 01.12.2004

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abstract = "For a Sperner family A ⊆ 2[n] let Ai denote the family of all i-element sets in A. We sharpen the LYM inequality ∑i |Ai|/(in) ≤ 1 by adding to the LHS all possible products of fractions |Ai|/(i n), with suitable coefficients. A corresponding inequality is established also for the linear lattice and the lattice of subsets of a multiset (with all elements having the same multiplicity).",

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N2 - For a Sperner family A ⊆ 2[n] let Ai denote the family of all i-element sets in A. We sharpen the LYM inequality ∑i |Ai|/(in) ≤ 1 by adding to the LHS all possible products of fractions |Ai|/(i n), with suitable coefficients. A corresponding inequality is established also for the linear lattice and the lattice of subsets of a multiset (with all elements having the same multiplicity).

AB - For a Sperner family A ⊆ 2[n] let Ai denote the family of all i-element sets in A. We sharpen the LYM inequality ∑i |Ai|/(in) ≤ 1 by adding to the LHS all possible products of fractions |Ai|/(i n), with suitable coefficients. A corresponding inequality is established also for the linear lattice and the lattice of subsets of a multiset (with all elements having the same multiplicity).

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Polynomial LYM inequalities

Abstract

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