Timeline for Matrix version of number theoretic integral lattice claim
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2012 at 0:08 | comment | added | Will Jagy | @Gerry, thanks, I did wonder if it were a sort of extended pigeonhole argument. | |
| May 31, 2012 at 23:07 | comment | added | Gerry Myerson | Will, a row for each man, a column for each woman, a zero for each incompatible couple. There's a set of $a$ men with at most $n-b$ compatible women, and $a+b\ge n+1$ implies $a\gt n-b$, so there is no pairing off of men with women that doesn't involve an incompatible couple. So there is no term in the determinant without a zero. | |
| May 31, 2012 at 20:45 | comment | added | Will Jagy | @Gerry, I looked up Hall's Marriage Theorem but cannot fill in the argument. | |
| May 31, 2012 at 20:38 | comment | added | Will Jagy | Alright, for prime $p | r,$ the rank of $D'$ and $D$ are the same $\pmod p,$ so the same applies to $P$ and $Q_1.$ I think that is the final piece of the puzzle. | |
| May 31, 2012 at 7:05 | comment | added | Gerry Myerson | Will, the observation two comments up can be understood in terms of Hall's Marriage Theorem. | |
| May 31, 2012 at 4:22 | comment | added | Will Jagy | @Gerhard, I still think the selfmobile has a future, I just need some venture capital. | |
| May 31, 2012 at 4:17 | comment | added | Will Jagy | @Gerhard, now I must leave it in place. I know where David works. Right, I get a little typing difference with inverses or not for $S,T$ but no matter. That is a new one on me, if we have a square matrix over a field with a rectangular $a \times b$ block of nothing but $0'$s, and $a + b \geq n+1,$ the the matrix is singular. Very nice. | |
| May 31, 2012 at 4:14 | vote | accept | Will Jagy | ||
| May 31, 2012 at 4:07 | comment | added | Gerhard Paseman | Please excuse Will, sometimes he is slow on the uptake. Only the other day I was reading a post of his about an idea on propulsion he was considering: the selfmobile. Gerhard "Not Always Faster Than Will" Paseman, 2012.05.30 | |
| May 31, 2012 at 3:30 | comment | added | Will Jagy | Printed out to study with my little brain. You know, if nobody has told you, you are really quite good at this, you ought to consider a career in mathematics. | |
| May 31, 2012 at 3:11 | history | answered | David E Speyer | CC BY-SA 3.0 |