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

Sho Suda, Hajime Tanaka

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)342-348
Number of pages7
JournalBulletin of the London Mathematical Society
Volume46
Issue number2
DOIs
Publication statusPublished - 2014 Apr

ASJC Scopus subject areas

  • Mathematics(all)

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