Inverse problems of the Erdős-Ko-Rado type theorems for families of vector spaces and permutations

Kong, Xiangliang; Xi, Yuanxiao; Qian, Bingchen; Ge, Gennian

doi:10.1007/s11425-020-1829-6

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2022

2023

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“…In [5], using the t-covering number, the authors described the structure of maximal non-trivial t-intersecting families of V k with large size, from which the extremal non-trivial t-intersecting families are determined (see also [8] for the latter result). Recently, in [16], the authors considered an inverse problem for t-intersecting families of subspaces, and provided structural characterizations for the families with maximal total intersection number.…”

Section: Introductionmentioning

confidence: 99%

$r$-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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Section: Introductionmentioning

confidence: 99%