Families of vector spaces with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>r</mml:mi></mml:math>-wise <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi mathvariant="script">L</mml:mi></mml:math>-intersections

Xiao, Jimeng; Liu, Jiuqiang; Zhang, Shenggui

doi:10.1016/j.disc.2018.01.007

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“…When t = 1 in Theorem 1.3, our result can be viewed as a vector space version of the result in [18]. We also refer the readers to [1,9,17,24] for the upper bounds of an r-wise L-intersecting families for vector spaces, where L is a set of non-negative integers.…”

Section: Introductionmentioning

confidence: 92%

$r$-cross $t$-intersecting families for vector spaces

Cao¹,

Lu²,

Lv³

et al. 2022

Preprint

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Let V be an n-dimensional vector space over the finite field F q , and V k denote the family of all k-dimensional subspaces of V . The familiesIn this paper, we first determine the structure of r-cross tintersecting families with maximum product of their sizes. As a consequence, we partially prove one of Frankl and Tokushige's conjectures about r-cross 1-intersecting families for vector spaces. Then we describe the structure of non-trivial r-cross t-intersecting families F 1 , F 2 , . . . , F r with maximum product of their sizes under the assumptions r = 2 andrespectively, where the F in the latter assumption is well known as r-wise t-intersecting family. Meanwhile, stability results for non-trivial r-wise t-intersecting families are also been proved.

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