Timeline for Counting transitive generators according to coset type
Current License: CC BY-SA 3.0
24 events
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| S Mar 4, 2018 at 19:25 | history | bounty ended | CommunityBot | ||
| S Mar 4, 2018 at 19:25 | history | notice removed | CommunityBot | ||
| S Feb 24, 2018 at 17:42 | history | bounty started | Marcel | ||
| S Feb 24, 2018 at 17:42 | history | notice added | Marcel | Draw attention | |
| S Feb 13, 2018 at 17:14 | history | bounty ended | thedude | ||
| S Feb 13, 2018 at 17:14 | history | notice removed | thedude | ||
| Feb 9, 2018 at 17:25 | history | edited | thedude | CC BY-SA 3.0 |
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| Feb 9, 2018 at 12:34 | answer | added | Marcel | timeline score: 1 | |
| Feb 8, 2018 at 11:36 | history | edited | thedude | CC BY-SA 3.0 |
provided proof for a partial result
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| Feb 6, 2018 at 17:42 | history | edited | thedude | CC BY-SA 3.0 |
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| S Feb 6, 2018 at 17:41 | history | bounty started | thedude | ||
| S Feb 6, 2018 at 17:41 | history | notice added | thedude | Draw attention | |
| Feb 3, 2018 at 23:35 | comment | added | YCor | Btw a few more rows for the second triangle would be welcome to get some intuition, if you did the computation. | |
| Feb 3, 2018 at 18:22 | comment | added | YCor | OK thanks, I got it. It amounts to count those $\pi$ such that $\langle\sigma,\pi\rangle$ acts transitively, according to the partition type induced by the orbits of its subgroup $\langle\sigma,\pi\sigma\pi^{-1}\rangle$. | |
| Feb 3, 2018 at 18:08 | comment | added | thedude | Ah, sorry about that. I didn't want to overburden the question with definitions. Coset type is defined in the classical book by MacDonald, or (very quickly) in section 2.1 of this paper: arxiv.org/pdf/1601.08206.pdf | |
| Feb 3, 2018 at 17:59 | comment | added | YCor | The coset set $S_{2n}/H_n$ has cardinal $\frac{(2n)!}{n!2^n}$; it identifies to the set of partitions of $2n$ elements into $n$ classes of cardinal 2. What is the the meaning of "coset type"? More precisely, given a partition $\lambda$ of $n$ and $\pi\in S_{2n}$, what do you mean by $\pi$ being of coset type $\lambda$? I'm not familiar with this vocabulary. | |
| Feb 3, 2018 at 17:46 | history | edited | thedude | CC BY-SA 3.0 |
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| Feb 3, 2018 at 17:42 | comment | added | YCor | I've read your first sentence "I want to count permutations"... which is confusing. Please edit to clarify. | |
| Feb 3, 2018 at 17:36 | comment | added | thedude | @YCor It is not from integers to integers, because I am breaking down according to coset type. So it is a function from partitions to integers. | |
| Feb 3, 2018 at 17:33 | comment | added | YCor | Maybe try to formulate things better. You're asking for a function from integers to integers (the number $p_n$ of those $\pi$ such that $\sigma,\pi$ generate a transitive subgroup on $2n$ elements), and then you're listing something which doesn't appear to just be a function from integers to integers... | |
| Feb 3, 2018 at 17:30 | answer | added | YCor | timeline score: 3 | |
| Feb 3, 2018 at 16:45 | history | edited | YCor |
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| Feb 3, 2018 at 14:42 | history | edited | thedude | CC BY-SA 3.0 |
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| Feb 3, 2018 at 14:36 | history | asked | thedude | CC BY-SA 3.0 |