A cross‐intersection theorem for vector spaces based on semidefinite programming
A cross‐intersection theorem for vector spaces based on semidefinite programming
复制标题
基于半定规划的向量空间交叉定理
DOI：
10.1112/blms/bdt101
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发表时间：
2013
影响因子：
0.9
通讯作者：
Hajime Tanaka
中科院分区：
文献类型：
--
作者：
Sho Suda;Hajime Tanaka
设F和G分别是有限域Fq上给定n维向量空间的k维和n维子空间族。设对所有x∈F和y∈G，x ∈ y ∈ 0。通过显式地构造半定规划问题的最优可行解，该问题类似于Lovász的theta函数，我们证明了，|F|| G| n−1k−1n−1还建立了极值族的特征。
Let F and G be families of k ‐ and ℓ ‐dimensional subspaces, respectively, of a given n ‐dimensional vector space over a finite field Fq . Suppose that x∩y≠0 for all x∈F and y∈G . By explicitly constructing optimal feasible solutions to a semidefinite programming problem which is akin to Lovász's theta function, we show that |F||G|⩽n−1k−1n−1ℓ−1 , provided that n⩾2k and n⩾2ℓ . The characterization of the extremal families is also established.