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Incidence Matrices of Subsets—A Rank Formula

✍ Scribed by Linial, Nathan; Rothschild, Bruce L.


Book ID
118212393
Publisher
Society for Industrial and Applied Mathematics
Year
1981
Weight
663 KB
Volume
2
Category
Article
ISSN
0196-5212

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It is well known that for every finite linear space the number b of lines is greater or equal to the number v of points of the space. In this paper we investigate the relation between the nonnegative integer b -v and suitable configurations of subspaces of a linear space.

On the Rank of Certain Incidence Matrice
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Let V be a vector space of dimension n ≥ 3 over GF(2). We are concerned with the incidence of k-dimensional subspaces in (k + 2)-dimensional subspaces where 1 ≤ k ≤ n -2. We compute here an upper bound for the rank of the associated incidence matrices over GF(2).