Covers in 4-uniform Intersecting Families with Covering Number Three

Chiba, Shuya; Furuya, Michitaka; Matsubara, Ryota; Takatou, Masanori

doi:10.3836/tjm/1342701352

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2020

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“…Their results showed that any non-trivial intersecting family with maximum size must have covering number 2. Over the years, there have been some results about covering number of intersecting family, see [3,5,8,10,12].…”

Section: Introductionmentioning

confidence: 99%

Intersecting families of vector spaces with maximum covering number

Gong,

Lv,

Wang

2020

Preprint

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Let V be an n-dimensional vector space over the finite field F q . Suppose that F is an intersecting family of m-dimensional subspaces of V . The covering number of F is the minimum dimension of a subspace of V which intersects all elements of F. In this paper, we give the tight upper bound for the size of F whose covering number is m, and describe the structure of F which reaches the upper bound. Moreover, we determine the structure of an maximum intersecting family of singular linear space with the maximum covering number.

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Section: Introductionmentioning

confidence: 99%