Timeline for Counting transitive generators according to coset type
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2018 at 19:11 | comment | added | thedude | That sequence does not refer to permutations, but sequence oeis.org/A000698, which is twice that, is said to be "the number of indecomposable perfect matchings on [2n]", which seems related | |
| Feb 3, 2018 at 21:46 | comment | added | YCor | I have no claim about the refinement! Thanks for the computation; then $p_n/(2^n(n-1)!)$ is very likely to be given by oeis.org/A004208 (I have checked in addition that the 6th term $p_6/7680=55205$ matches). Interestingly, the Sloane definition does not refer to permutations. | |
| Feb 3, 2018 at 18:58 | comment | added | thedude | Your solution predicts $p_5/768=4081$ and it looks perfectly correct to me. Sadly, I don't see how to refine it to account for coset type. | |
| Feb 3, 2018 at 18:43 | comment | added | YCor | PS the first few terms of $p_n/(2^n(n-1)!)$, $n\ge 1$, according to the OP's post (just summing the rows of the second triangle) are 1, 5, 37, 353. Or equivalently $((2n)!-p_n)//(2^n(n-1)!)$ is given by 0, 1, 8, 67. I found both sequences in Sloane with 2 solutions and extrapolation to $n=5$ gives 4 possible candidates for $p_5/2^54!=p_5/768$: 4081, 4123, 4165, 4315. If anyone has something to run an easy program and compute the genuine value of $p_5/768$, it would be useful! | |
| Feb 3, 2018 at 17:30 | history | answered | YCor | CC BY-SA 3.0 |