Singular 0/1-Matrices, and the Hyperplanes Spanned by Random 0/1-Vectors
نویسندگان
چکیده
Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =
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Let Ps(d) be the probability that a random 0/1-matrix of size d× d is singular, and let E(d) be the expected number of 0/1-vectors in the linear subspace spanned by d − 1 random independent 0/1-vectors. (So E(d) is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on Ps(d) are equivalent to bounds on E(d): Ps(d) =
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 15 شماره
صفحات -
تاریخ انتشار 2006