On sets of vectors of a finite vector space in which every subset of basis size is a basis
نویسندگان
چکیده
منابع مشابه
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set S of vectors of a k-dimensional vector space over Fq, 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 = ph 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 va...
متن کاملOn sets of vectors of a finite vector space in which every subset of basis size is a basis II
This article contains a proof of the MDS conjecture for k ≤ 2p− 2. That is, that if S is a set of vectors of Fq in which every subset of S of size k is a basis, where q = p, p is prime and q is not and k ≤ 2p − 2, then |S| ≤ q + 1. It also contains a short proof of the same fact for k ≤ p, for all q.
متن کامل2 8 Ja n 20 12 On sets of vectors of a finite vector space in which every subset of basis size is a basis II ∗
This article contains a proof of the MDS conjecture for k ≤ 2p− 2. That is, that if S is a set of vectors of Fq in which every subset of S of size k is a basis, where q = p, p is prime and q is not and k ≤ 2p − 2, then |S| ≤ q + 1. It also contains a short proof of the same fact for k ≤ p, for all q.
متن کاملOn Large Subsets of a Finite Vector Space in Which Every Subset of Basis Size Is a Basis
It is shown that the maximum size of a set S of vectors of a k-dimensional vector space over Fq, with the property that every subset of size k is a basis, is at most q + 1, if k is bounded above by the characteristic p, and at most q + k − p, if k ≥ 4 is larger than the characteristic. Moreover, for 3 ≤ k ≤ p, the sets S of maximum size are classified. These results have various implications. O...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2012
ISSN: 1435-9855
DOI: 10.4171/jems/316