A cross-intersection theorem for vector spaces based on semidefinite programming

Sho Suda, Hajime Tanaka

研究成果: Article査読

7 被引用数 (Scopus)

抄録

Let ℱ and G{script} be families of k- and ℓ-dimensional subspaces, respectively, of a given n-dimensional vector space over a finite field F{double-struck}q. Suppose that x ∩ y ≠ 0 for all x ∈ ℱ and y ∈ G{script}. By explicitly constructing optimal feasible solutions to a semidefinite programming problem which is akin to Lovász's theta function, we show that (Equation Presented), provided that n ≥ 2k and n ≥ 2 ℓ. The characterization of the extremal families is also established.

本文言語English
ページ(範囲)342-348
ページ数7
ジャーナルBulletin of the London Mathematical Society
46
2
DOI
出版ステータスPublished - 2014 4

ASJC Scopus subject areas

  • 数学 (全般)

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