Timeline for Is Carlitz's paper correct about the number of similarity classes of commuting matrices?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2020 at 13:13 | vote | accept | Yifeng Huang | ||
| Aug 28, 2020 at 10:40 | history | became hot network question | |||
| Aug 28, 2020 at 6:08 | answer | added | darij grinberg | timeline score: 17 | |
| Aug 28, 2020 at 0:21 | comment | added | Yifeng Huang | @darijgrinberg This does answer the question and is all I need. Could you put it as an answer? | |
| Aug 27, 2020 at 23:09 | history | edited | LSpice | CC BY-SA 4.0 |
Missed a typo; put author in title
|
| Aug 27, 2020 at 23:05 | comment | added | LSpice | … $\operatorname{GF}(q)$, where $A_i$ runs through a complete set of nonsimilar matrices, and, for each $A_i$, $B_i$ commutes with $A_i$. \\ Thus the problem of determining the number of classes of pairs of commuting matrices remains open.") | |
| Aug 27, 2020 at 23:05 | comment | added | LSpice | (The relevant correction is a tiny note at the very end of @darijgrinberg's link: "J. Towber has kindly pointed out to the writer that there is an error in the paper: …. The error occurs in equation (5) of the paper. The results of the paper remain valid if we redefine $Q(n)$ as equal to the number of pairs of $n\times n$ matrices $(A_i, B_i)$, with elements in … | |
| Aug 27, 2020 at 23:00 | history | edited | LSpice | CC BY-SA 4.0 |
Name of paper
|
| Aug 27, 2020 at 22:26 | comment | added | Pedro | Ah, I see. @darijgrinberg Doesn't that provide an answer to the question in the title? | |
| Aug 27, 2020 at 22:03 | comment | added | darij grinberg | It is wrong. See the correction published in AMM 71 (1964), issue 8, page 900. Unfortunately this was published in the "Mathematical Notes" section, making it hard to find (as these notes don't get DOIs of their own). | |
| Aug 27, 2020 at 20:52 | history | edited | Yifeng Huang | CC BY-SA 4.0 |
add the place where the proof has a gap
|
| Aug 27, 2020 at 20:50 | comment | added | Yifeng Huang | The equation (4) computes the number of solutions of AX=XA for A in a fixed similarity class, and concludes in (5) that if we sum up such numbers over all possible similarity classes of A, we get the answer. This assumes that if X and X' are different, then (A,X) and (A,X') always contribute to different simultaneous similarity classes. | |
| Aug 27, 2020 at 19:51 | comment | added | Pedro | Could you point out where this happens in the proof? I scanned the paper and failed to find it. | |
| Aug 27, 2020 at 19:45 | history | asked | Yifeng Huang | CC BY-SA 4.0 |