Timeline for Lifting matrices mod 2 to integers.
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2018 at 20:12 | comment | added | Per Alexandersson | The weaker question w Stanley's answer is a great competition problem! | |
| Mar 15, 2010 at 15:36 | answer | added | HenrikRüping | timeline score: 2 | |
| Mar 15, 2010 at 4:46 | comment | added | Mikola | Whoops! I totally messed that up, you are correct. | |
| Mar 15, 2010 at 1:40 | answer | added | Richard Stanley | timeline score: 26 | |
| Mar 15, 2010 at 1:18 | comment | added | Jonas Meyer | Mikola, [[0,1],[1,0]] has determinant -1 but changing the sign of a one yields determinant 1. | |
| Mar 15, 2010 at 1:14 | comment | added | Petya | Mikola, could you please explain why it must be congruent to 1 modulo 6 and what is the connection with the Chinese remainder theorem? | |
| Mar 15, 2010 at 1:09 | comment | added | Mikola | Having the original determinant be odd is not sufficient. At the very least, it must be congruent to 1 modulo 6, by the Chinese remainder theorem. Don't know if this helps much or not... | |
| Mar 15, 2010 at 1:07 | history | edited | Petya | CC BY-SA 2.5 |
edited body
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| Mar 15, 2010 at 0:33 | comment | added | Harry Gindi | No luck finding a counterexample or no luck finding an example? | |
| Mar 15, 2010 at 0:30 | comment | added | Mariano Suárez-Álvarez | I;ve just tried a brute search for the first version, generating random $01$-matrices. No luck for smallish values of $n$... | |
| Mar 15, 2010 at 0:26 | comment | added | Pete L. Clark | @Petya: I was rather asking if you had tried a computer search, and if so how far. As for why you should look specifically at matrices whose determinant is large...no particular reason, except that these are already tabulated in many easily available places. | |
| Mar 15, 2010 at 0:14 | comment | added | Petya | @Pete, I tried to construct a counterexample by hands (I also suppose that answer is negative). Could you, please, explain me why one should try to search a counterexample through matrices with large odd determinant? | |
| Mar 15, 2010 at 0:12 | comment | added | Pete L. Clark | Also the title of your question was confusing to me. Your weaker question has something to do with lifting matrices mod 2 (except that you do not want to change the zero entries by even integers), but your stronger question has nothing to do with it, so far as I can see. | |
| Mar 15, 2010 at 0:07 | comment | added | Pete L. Clark | I would guess that this (your first question) is unlikely to be true. How hard have you tried to search for a counterexample, either by pure brute force search or by a targeted search of 0-1 matrices with large odd determinant? C.f. mathworld.wolfram.com/HadamardsMaximumDeterminantProblem.html | |
| Mar 14, 2010 at 23:56 | history | asked | Petya | CC BY-SA 2.5 |