Timeline for When is a 0-1 matrix a one-intersection incidence matrix?
Current License: CC BY-SA 3.0
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| Jun 2, 2013 at 13:04 | comment | added | Will Sawin | No. I am claiming that if $M$ is not realizable by straight lines, then removing such a row or column will not make it realizable. The reason for this should hopefully be clear, but since some things are realizable by curves and not straight lines, this can only provide a lower bound. By the way, I think the next couple arrangements to check are affine space over $\mathbb F_3$ and affine space over $\mathbb F_3$ minus a point. Can these be realizes by curves? | |
| Jun 2, 2013 at 12:32 | comment | added | Seva | For your lower-bounding argument, do you claim that if $M$ is not realizable, then a matrix obtained from $M$ by removing a row with just two $1$s is not realizable either? If so, could you explain? (From a realization of the "shortened matrix", say $M'$, how can one get a realization of the original matrix $M$? Just adding a line segment may not work, as the realization of $M'$ can potentially involve curves which are not segments. It is not true that if a matrix is realizable, then it is realizable with segments only.) Similarly, why can one remove weight-$2$ columns? | |
| Jun 2, 2013 at 2:08 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jun 2, 2013 at 1:04 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jun 1, 2013 at 23:04 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jun 1, 2013 at 22:44 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jun 1, 2013 at 22:23 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jun 1, 2013 at 22:05 | history | answered | Will Sawin | CC BY-SA 3.0 |