Timeline for Number of $\{0,1\}$ matrices with distinct rows and distinct columns
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2016 at 0:37 | comment | added | Pat Devlin | Disclaimer: With the rank stuff, you quickly get into the world of a bunch of conjectures. For example, search something like "probability 0,1 matrix has zero determinant". This ought to be essentially the probability that the thing has two identical rows, but even proving it was exponentially small was tricky. | |
| Dec 29, 2016 at 0:16 | comment | added | Pat Devlin | Yes to the first question. For rank $m$ the count drops drastically. Almost all matrices have full rank. Degeneracy in rank is mostly due to repeated rows, so counting matrices with only $m$ different rows should be pretty close to the number of matrices with rank $m$. If you want low rank and all distinct rows, I'm not sure what to expect there. | |
| Dec 29, 2016 at 0:04 | comment | added | user94040 | So $2^{rc}$ and $\frac{2^{rc}}{r!c!}$ roughly? Can I ask what happens if I restrict the rank to exactly $m$ and ask similar count? | |
| Dec 28, 2016 at 23:44 | history | edited | Pat Devlin | CC BY-SA 3.0 |
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| Dec 28, 2016 at 23:38 | history | answered | Pat Devlin | CC BY-SA 3.0 |