Timeline for Special permutations of $\{1,2,3,\ldots,n\}$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2021 at 6:15 | comment | added | BookWick | @VladimirDotsenko How did Flajolet and Sedgewick get the below generating function for the Hertzsprung problem (this is the problem which you gave answer to here)? $$\sum_{n=0}^\infty n! x^n \frac{(1-x)^n}{(1+x)^n}$$ | |
| Mar 7, 2021 at 23:25 | comment | added | Gerry Myerson | You have the option, BookWick, of "accepting" this answer by clicking in the check mark next to it. | |
| Mar 7, 2021 at 12:39 | comment | added | BookWick | You're fabulous! I figured out the mistake in OEIS formula. Thanks man, I really appreciate your time, efforts for dealing with a complete noob like me. Thanks! I really appreciate it! | |
| Mar 7, 2021 at 12:16 | comment | added | Vladimir Dotsenko | What exactly is your point? Your formula gives a wrong answer for $n=2$. The formula in my answer gives the correct answer, and plus it comes with a proof. What else do you need, really? | |
| Mar 7, 2021 at 10:53 | comment | added | BookWick | What about $n = 4$? The answer should be 2 right? I guess both the formulas give the answer 2 don't they? Thanks for your efforts and time. | |
| Mar 7, 2021 at 10:42 | comment | added | Vladimir Dotsenko | @SarthChavan you can apply your formula for $n=2$. It will give you the answer $2-2+2=2$, while the formula I give in my answer gives the correct answer $2-4+2=0$. So congratulations, you found a misprint in OEIS. | |
| Mar 7, 2021 at 10:29 | comment | added | BookWick | In the OEIS formula it's $$\dbinom{n - k}{i}$$ However you are claiming that it should be $$\dbinom{n - k + 1}{i}$$ I don't get this part. Thanks! | |
| Mar 7, 2021 at 9:40 | history | edited | Vladimir Dotsenko | CC BY-SA 4.0 |
added details
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| Mar 7, 2021 at 9:27 | comment | added | Vladimir Dotsenko | @BooleanCoder I clarified what the argument gives for $U_{n,k}$, and I will try to write the rest in more detail, though it would be good if you can ask a more specific question, not just "I don't get...". | |
| Mar 7, 2021 at 9:26 | history | edited | Vladimir Dotsenko | CC BY-SA 4.0 |
deleted 28 characters in body
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| Mar 7, 2021 at 9:16 | comment | added | BookWick | Also what did you get $U_{n,k}$? I mean I know what it denotes but what did you get $U_{n,k}$ in terms of the sum? Also what should be the correct formula? Thanks | |
| Mar 7, 2021 at 8:30 | history | answered | Vladimir Dotsenko | CC BY-SA 4.0 |