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On sets of vectors of a finite vector space in which every subset of basis size is a basis

2012
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Journal of the European Mathematical Society (Print)
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It is shown that the maximum size of a set S of vectors of a k-dimensional vector space over F q , with the property that every subset of size k is a basis, is at most q + 1 if k ≤ p, and at most q + k − p if q ≥ k ≥ p + 1 ≥ 4, where q = p h and p is prime. Moreover, for k ≤ p, the sets S of maximum size are classified, generalising Beniamino Segre's "arc is a conic" theorem. These results have various implications. One such implication is that a k × (p + 2) matrix, with k ≤ p and entries from

doi:10.4171/jems/316
fatcat:huib5strkjcthcqnd7dpywja24