Partitions of vector spaces
نویسندگان
چکیده
منابع مشابه
On Partitions of Finite vector Spaces
In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that the number of the subspaces of minimum dimension t of a non-trivial partition of Vn(q) is greater than or equal to q + t. Moreover, we give some extensions of a well known Beutelspacher-Heden’s result on existence of T -partitions.
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Let d, r ∈ N and ‖ · ‖ be any norm on Rd . Let B denote the unit ball with respect to this norm. We show that any sequence v1, v2, . . . of vectors in B can be partitioned into r subsequences V1, . . ., Vr in a balanced manner with respect to the partial sums: For all n ∈ N, r , we have ‖∑i k,vi∈V vi − r ∑i k vi‖ 2.0005d. A similar bound holds for partitioning sequences of vector sets. Both res...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1990-1021207-2