Timeline for Number of Permutations?
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2020 at 23:27 | comment | added | Sam Hopkins | The same question was asked many years later as: mathoverflow.net/questions/371538/…. | |
| Feb 19, 2017 at 21:38 | answer | added | Max Alekseyev | timeline score: 0 | |
| Oct 18, 2013 at 23:53 | answer | added | Ira Gessel | timeline score: 5 | |
| Oct 16, 2013 at 19:53 | comment | added | Ira Gessel | As I recall, this problem is discussed in Riordan's Introduction to Combinatorial Analysis, but I don't have my copy handy. You might also be able to find some relevant references by searching for "discordant permutations". On another aspect of the question, although the number of possible $\tau$ depends on $\sigma$, this number is close to $n!/e^2$ independently of $\sigma$. Stronger asymptotic results on the number of ways to add a row to a Latin rectangle can be found in C. D. Godsil, and B. D. McKay, Asymptotic enumeration of Latin rectangles. J. Combin. Theory Ser. B 48 (1990), 19–44. | |
| Oct 16, 2013 at 11:16 | answer | added | Peter Mueller | timeline score: 6 | |
| Oct 16, 2013 at 1:35 | comment | added | Timothy Chow | Right. The OP's description seems perfectly clear to me and makes it obvious that we're talking about 3xn Latin rectangles. Had it originally been stated in terms of fpf permutations, I would probably have had to think a bit before realizing that it was a question about Latin rectangles in disguise. | |
| Oct 15, 2013 at 23:39 | comment | added | Todd Trimble | @WlodzimierzHolsztynski It just means there are no repetitions in any column. | |
| Oct 15, 2013 at 23:09 | answer | added | Yuichiro Fujiwara | timeline score: 8 | |
| Oct 15, 2013 at 22:41 | comment | added | Włodzimierz Holsztyński | What does "each column must have unique elements" mean? However, @Todd+Peter's reformulation makes it fine. | |
| S Oct 15, 2013 at 22:34 | history | suggested | CommunityBot | CC BY-SA 3.0 |
proper use of \le
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| Oct 15, 2013 at 22:28 | review | Suggested edits | |||
| S Oct 15, 2013 at 22:34 | |||||
| Oct 15, 2013 at 22:26 | comment | added | Timothy Chow | I see nothing poorly stated or off-topic about the question. | |
| Oct 15, 2013 at 22:25 | answer | added | Timothy Chow | timeline score: 14 | |
| Oct 15, 2013 at 20:30 | comment | added | Gerhard Paseman | More naturally, this is counting Latin rectangles with the first two rows specified. It strikes me as a kind of "Project Euler" problem, and one might take care before responding. (See a post on meta talking about not answering such problems.) Gerhard "Off To Do Some Writing" Paseman, 2013.10.15 | |
| Oct 15, 2013 at 16:38 | history | edited | user9072 |
edited tags
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| Oct 15, 2013 at 16:02 | history | edited | Todd Trimble | CC BY-SA 3.0 |
added 417 characters in body
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| Oct 15, 2013 at 15:52 | comment | added | Todd Trimble | Yes, it's not exactly stated in a professional manner, but the problem could probably be rephrased to make it "MO-worthy". If you have a solution, @PeterMueller, it might be worth putting down (albeit it quickly! since the question looks doomed for closure at this rate). | |
| Oct 15, 2013 at 15:48 | comment | added | Peter Mueller | The question is certainly poorly stated, but I don't think that it is totally off-topic. Indeed, as Todd Trimble remarks, the question is: Let $\sigma$ be a fixed-point-free permutation. What is the number of fixed-point-free permutations $\tau$ such that $\sigma^{-1}\tau$ is fixed-point-free too? This number depends on $\sigma$ (as the OP remarked already). I only see how to compute this number via the character table of the symmetric group $S_N$. | |
| Oct 15, 2013 at 15:42 | review | Close votes | |||
| Oct 15, 2013 at 18:08 | |||||
| Oct 15, 2013 at 15:40 | comment | added | Todd Trimble | If we consider the analogous problem with two rows, we are computing the number of derangements, a classic problem (with a well-known solution). I ask those voting to close: is the case for three rows a straightforward extension of this problem? | |
| Oct 15, 2013 at 15:32 | review | First posts | |||
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| Oct 15, 2013 at 15:15 | history | asked | balli | CC BY-SA 3.0 |