Timeline for Encoding primes via ranks of sign matrices
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2023 at 17:33 | comment | added | math54321 | @ThomasSauvaget Good point - for instance $A_n$ has trace zero iff $n \equiv 2 \pmod 4$. I also computed some characteristic polynomials, but did not see any patterns at first glance | |
| Apr 1, 2023 at 4:15 | comment | added | Thomas Sauvaget | Side question : if primality is encoded by the number of non-zero eigenvalues, one can wonder what other properties are encoded in the rest of the spectrum. | |
| Mar 29, 2023 at 10:11 | comment | added | Thomas Sauvaget | Small remark : since it has been checked up to 1024, it is in particular true for the first Carmichael number (aka pseudo prime) 561, which adds some weight to the conjecture. | |
| Mar 28, 2023 at 7:34 | history | edited | Rodrigo de Azevedo | CC BY-SA 4.0 |
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| Mar 28, 2023 at 6:53 | comment | added | Maarten Havinga | @math54321 I see indeed, was too early with posting | |
| Mar 27, 2023 at 19:15 | comment | added | math54321 | @MaartenHavinga I don't think that $n = 8$ gives a Hadamard matrix. Indeed $A_8 A_8^T$ is not even diagonal | |
| Mar 27, 2023 at 18:18 | comment | added | Maarten Havinga | All I can add is that for $n=2^k$, it's the $n×n$ Hadamard matrix obtained from Sylvester's construction. However it does not give Hadamard matrices for other $n$. | |
| Mar 27, 2023 at 8:51 | answer | added | Per Alexandersson | timeline score: 1 | |
| Mar 23, 2023 at 18:18 | history | edited | math54321 | CC BY-SA 4.0 |
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| Mar 22, 2023 at 22:04 | answer | added | Peter Mueller | timeline score: 5 | |
| Mar 22, 2023 at 21:06 | comment | added | darij grinberg | No -- I was thinking that divisors of $n$ would lead to equal rows in $A$. | |
| Mar 22, 2023 at 20:25 | comment | added | math54321 | @darijgrinberg Maybe you were secretly thinking about $\dim \ker$ instead of rank :) Somewhat related, I don't know if there's a good way of viewing $A_n, A_m$ as blocks inside $A_{nm}$ | |
| Mar 22, 2023 at 19:55 | comment | added | darij grinberg | Curious! My intuition would have suggested that $A_n$ should have the smaller (not greater) rank the more divisors $n$ has, and yet it is apparently the other way round. | |
| S Mar 22, 2023 at 19:25 | review | First questions | |||
| Mar 22, 2023 at 19:42 | |||||
| S Mar 22, 2023 at 19:25 | history | asked | math54321 | CC BY-SA 4.0 |