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On sets of vectors of a finite vector space in which every subset of basis size is a basis II Vrije Universiteit Brussel
This article contains a proof of the MDS conjecture for k ? 2p ? 2. That is, that if S is a set of vectors of Fkq in which every subset of S of size k is a basis, where q = p h , 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.
On sets of vectors of a finite vector space in which every subset of basis size is a basis II Ghent University
This article contains a proof of the MDS conjecture for k a parts per thousand currency sign 2p - 2. That is, that if S is a set of vectors of in which every subset of S of size k is a basis, where q = p (h) , p is prime and q is not and k a parts per thousand currency sign 2p - 2, then |S| a parts per thousand currency sign q + 1. It also contains a short proof of the same fact for k a parts per thousand currency sign p, for all q.
Miklós-Manickam-Singhi conjectures on partial geometries Ghent University
In this paper we give a proof of the Mikls-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.
ABJ(M) and Fractional M2's with Fractional M2 Charge Vrije Universiteit Brussel
Recently Aharony, Bergman and Jafferis (ABJ) have argued that a 3d U(N+M)k × U(N)−k Chern-Simons gauge theory may have a vacuum with Script N = 6 supersymmetry only if M≤k and if a certain period of the B-field in a IIA background is quantized. We use a braneology argument to argue that Script N = 3 supersymmetry may be preserved under the weaker condition that 2Nk≥M(M−k) with no restriction on the B-field. IIB brane cartoons and 11d ...