Almost intersecting fami lies of sets

Dániel Gerbnert; Nathan Lemons; Cory Palmer; Balázs Patkós; Vajk Szécsi

doi:10.1137/120878744

Almost intersecting fami lies of sets

Dániel Gerbnert, Nathan Lemons, Cory Palmer, Balázs Patkós, Vajk Szécsi

Mathematical Sciences

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

14 Scopus citations

Abstract

Let us write D_F(G) = {F ∈ F: F ∩ G = φ} for a set G and a family F. Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |D _F(F)| ≤ l (|D_F(F)| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)-almost intersecting (l-almost intersecting) family F.

Original language	English
Pages (from-to)	1657-1669
Number of pages	13
Journal	SIAM Journal on Discrete Mathematics
Volume	26
Issue number	4
DOIs	https://doi.org/10.1137/120878744
State	Published - 2012

Keywords

Extremal set theory
Intersection theorems
Sperner-type theorems

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10.1137/120878744

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title = "Almost intersecting fami lies of sets",

abstract = "Let us write DF(G) = \{F ∈ F: F ∩ G = φ\} for a set G and a family F. Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |D F(F)| ≤ l (|DF(F)| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)-almost intersecting (l-almost intersecting) family F.",

keywords = "Extremal set theory, Intersection theorems, Sperner-type theorems",

author = "D{\'a}niel Gerbnert and Nathan Lemons and Cory Palmer and Bal{\'a}zs Patk{\'o}s and Vajk Sz{\'e}csi",

year = "2012",

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language = "English",

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T1 - Almost intersecting fami lies of sets

AU - Gerbnert, Dániel

AU - Lemons, Nathan

AU - Palmer, Cory

AU - Patkós, Balázs

AU - Szécsi, Vajk

PY - 2012

Y1 - 2012

N2 - Let us write DF(G) = {F ∈ F: F ∩ G = φ} for a set G and a family F. Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |D F(F)| ≤ l (|DF(F)| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)-almost intersecting (l-almost intersecting) family F.

AB - Let us write DF(G) = {F ∈ F: F ∩ G = φ} for a set G and a family F. Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |D F(F)| ≤ l (|DF(F)| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)-almost intersecting (l-almost intersecting) family F.

KW - Extremal set theory

KW - Intersection theorems

KW - Sperner-type theorems

UR - https://www.scopus.com/pages/publications/84871534775

U2 - 10.1137/120878744

DO - 10.1137/120878744

M3 - Article

AN - SCOPUS:84871534775

SN - 0895-4801

VL - 26

SP - 1657

EP - 1669

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -

Almost intersecting fami lies of sets

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Keywords

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