Shadows and intersections in vector spaces

Ameera Chowdhury; Balázs Patkós

doi:10.1016/j.jcta.2009.10.010

Shadows and intersections in vector spaces

Ameera Chowdhury
, Balázs Patkós

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

42 Scopus citations

Abstract

We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. We apply this result to extend Frankl's theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erdo{double acute}s-Ko-Rado theorem for vector spaces.

Original language	English (US)
Pages (from-to)	1095-1106
Number of pages	12
Journal	Journal of Combinatorial Theory. Series A
Volume	117
Issue number	8
DOIs	https://doi.org/10.1016/j.jcta.2009.10.010
State	Published - Nov 2010
Externally published	Yes

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (A. Chowdhury), [email protected] (B. Patkós). 1 Supported by NSF Grant #: CCF-0728928.

Funding Information:
The first author thanks the NSF for supporting her and the Rényi Institute for hosting her while she was an NSF-CESRI fellow during the summer of 2008. We also thank Jacques Verstraëte for carefully reading this manuscript.

Keywords

Erdo{double acute}s-Ko-Rado
Intersecting family
Kruskal-Katona
Shadow
Vector space

Publisher link

10.1016/j.jcta.2009.10.010

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title = "Shadows and intersections in vector spaces",

abstract = "We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lov{\'a}sz. We apply this result to extend Frankl's theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erdo\{double acute\}s-Ko-Rado theorem for vector spaces.",

keywords = "Erdo\{double acute\}s-Ko-Rado, Intersecting family, Kruskal-Katona, Shadow, Vector space",

author = "Ameera Chowdhury and Bal{\'a}zs Patk{\'o}s",

note = "Funding Information: E-mail addresses: [email protected] (A. Chowdhury), [email protected] (B. Patk{\'o}s). 1 Supported by NSF Grant \#: CCF-0728928. Funding Information: The first author thanks the NSF for supporting her and the R{\'e}nyi Institute for hosting her while she was an NSF-CESRI fellow during the summer of 2008. We also thank Jacques Verstra{\"e}te for carefully reading this manuscript.",

year = "2010",

month = nov,

doi = "10.1016/j.jcta.2009.10.010",

language = "English (US)",

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pages = "1095--1106",

journal = "Journal of Combinatorial Theory. Series A",

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AU - Chowdhury, Ameera

AU - Patkós, Balázs

N1 - Funding Information: E-mail addresses: [email protected] (A. Chowdhury), [email protected] (B. Patkós). 1 Supported by NSF Grant #: CCF-0728928. Funding Information: The first author thanks the NSF for supporting her and the Rényi Institute for hosting her while she was an NSF-CESRI fellow during the summer of 2008. We also thank Jacques Verstraëte for carefully reading this manuscript.

PY - 2010/11

Y1 - 2010/11

N2 - We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. We apply this result to extend Frankl's theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erdo{double acute}s-Ko-Rado theorem for vector spaces.

AB - We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. We apply this result to extend Frankl's theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erdo{double acute}s-Ko-Rado theorem for vector spaces.

KW - Erdo{double acute}s-Ko-Rado

KW - Intersecting family

KW - Kruskal-Katona

KW - Shadow

KW - Vector space

UR - https://www.scopus.com/pages/publications/77955654874

UR - https://www.scopus.com/pages/publications/77955654874#tab=citedBy

U2 - 10.1016/j.jcta.2009.10.010

DO - 10.1016/j.jcta.2009.10.010

M3 - Article

AN - SCOPUS:77955654874

SN - 0097-3165

VL - 117

SP - 1095

EP - 1106

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 8

ER -

Shadows and intersections in vector spaces

Abstract

Bibliographical note

Keywords

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