Timeline for Distribution of sum of two permutation matrices
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 22, 2018 at 23:49 | vote | accept | Turbo | ||
| Sep 22, 2018 at 23:48 | vote | accept | Turbo | ||
| Sep 22, 2018 at 23:48 | |||||
| Sep 22, 2018 at 23:23 | comment | added | Turbo | @GjergjiZaimi This will definitely help. | |
| Sep 22, 2018 at 23:19 | comment | added | Gjergji Zaimi | @Freeman. I expanded the answer to contain the generating functions in all cases and how they are derived. Hope this helps. | |
| Sep 22, 2018 at 23:18 | history | edited | Gjergji Zaimi | CC BY-SA 4.0 |
added 2638 characters in body
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| Sep 22, 2018 at 20:36 | vote | accept | Turbo | ||
| Sep 22, 2018 at 20:37 | |||||
| Sep 22, 2018 at 20:36 | vote | accept | Turbo | ||
| Sep 22, 2018 at 20:36 | |||||
| Sep 22, 2018 at 17:36 | comment | added | Gjergji Zaimi | The general technique is outlined here en.wikipedia.org/wiki/Symbolic_method_(combinatorics) A great place to learn about it is Flajolet and Sedgewick's book Analytic Combinatorics. | |
| Sep 22, 2018 at 17:34 | comment | added | Gjergji Zaimi | @Freeman. It is a fundamental theorem in combinatorics. It roughly says that if $F(x)$ is the exponential generating function of some structures, then $e^F$ is the exponential generating function of disjoint unions of such structures. For the example above, I can find the exponential generating function of even cycles to be $F(x)=\frac{x^2}{2}+\frac{x^4}{4}+\cdots$ since there are exactly $(2n-1)!$ cycles of size $2n$. Therefore $e^{tF}$ is the exponential generating function of disjoint unions of even cycles, together with a statistic $t$ that keeps track of the number of cycles. | |
| Sep 22, 2018 at 9:39 | comment | added | Turbo | @GjergjiZaimi What exactly is the exponential formula? | |
| Sep 21, 2018 at 2:57 | comment | added | T. Amdeberhan | Accordingly, $f(2n+1,k)=0$ and $f(2n,k)=\frac1{n!}e_{n-k}(1,2,\dots,n-1)$ where $e_j$ is the elementary symmetric function of $1,2,\dots,n-1$. | |
| Sep 21, 2018 at 2:38 | history | edited | Gjergji Zaimi | CC BY-SA 4.0 |
added 230 characters in body
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| Sep 21, 2018 at 2:27 | history | answered | Gjergji Zaimi | CC BY-SA 4.0 |