On set systems without weak 3-Δ-subsystems

M. Axenovich; D. Fon-Der-Flaass; A. Kostochka

doi:10.1016/0012-365X(94)00185-L

On set systems without weak 3-Δ-subsystems

M. Axenovich, D. Fon-Der-Flaass, A. Kostochka

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

Abstract

A collection of sets is called a weak Δ-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function f_w(n), the maximal size of a collection of n-element sets no three of which form a weak Δ-system. Namely, we prove that, for every δ > 0. f_w(n) = 0(n!^{1 2 + b}).

Original language	English (US)
Pages (from-to)	57-62
Number of pages	6
Journal	Discrete Mathematics
Volume	138
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(94)00185-L
State	Published - Mar 6 1995
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(94)00185-L

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title = "On set systems without weak 3-Δ-subsystems",

abstract = "A collection of sets is called a weak Δ-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function fw(n), the maximal size of a collection of n-element sets no three of which form a weak Δ-system. Namely, we prove that, for every δ > 0. fw(n) = 0(n! 1 2 + b).",

author = "M. Axenovich and D. Fon-Der-Flaass and A. Kostochka",

note = "Funding Information: * Corresponding author. On leave from Institute of Mathematics, Novosibirsk, 630090, Russian Federation. 2 Supported by the grant 93-011-1486 of the Russian Fundamental Research Foundation.",

year = "1995",

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doi = "10.1016/0012-365X(94)00185-L",

language = "English (US)",

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AU - Axenovich, M.

AU - Fon-Der-Flaass, D.

AU - Kostochka, A.

N1 - Funding Information: * Corresponding author. On leave from Institute of Mathematics, Novosibirsk, 630090, Russian Federation. 2 Supported by the grant 93-011-1486 of the Russian Fundamental Research Foundation.

PY - 1995/3/6

Y1 - 1995/3/6

N2 - A collection of sets is called a weak Δ-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function fw(n), the maximal size of a collection of n-element sets no three of which form a weak Δ-system. Namely, we prove that, for every δ > 0. fw(n) = 0(n! 1 2 + b).

AB - A collection of sets is called a weak Δ-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function fw(n), the maximal size of a collection of n-element sets no three of which form a weak Δ-system. Namely, we prove that, for every δ > 0. fw(n) = 0(n! 1 2 + b).

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JF - Discrete Mathematics

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On set systems without weak 3-Δ-subsystems

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