Singular 0/1-matrices, and the hyperplanes spanned by random 0/1-vectors
| dc.creator | Voigt, Thomas | |
| dc.creator | Ziegler, Günter M. | |
| dc.date | 2003-08-06 | |
| dc.date | 2008-12-17 | |
| dc.date.accessioned | 2026-07-07T12:13:24Z | |
| dc.date.available | 2026-07-07T12:13:24Z | |
| dc.description | Let $P(d)$ be the probability that a random 0/1-matrix of size $d \times d$ 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 $P(d)$ are equivalent to bounds on $E(d)$: \[ P(d) = (2^{-d} E(d) + \frac{d^2}{2^{d+1}}) (1 + o(1)). \] We also report about computational experiments pertaining to these numbers. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308050 | |
| dc.identifier | http://arxiv.org/abs/math/0308050 | |
| dc.identifier | Combinatorics, Probability & Computing, 15:463-471, 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210832 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 15A52; 05B20; 05D40 | |
| dc.title | Singular 0/1-matrices, and the hyperplanes spanned by random 0/1-vectors | |
| dc.type | text |