Timeline for How many permutations for each sum of digits of a number of length l? (solved but asking for insight)
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 18, 2011 at 22:48 | vote | accept | mna | ||
| Feb 18, 2011 at 17:02 | comment | added | mna | You have convinced me thanks! Now taking a side-step, is there a simpler function than my f(t,L)? | |
| Feb 18, 2011 at 16:31 | comment | added | Tom De Medts | Yes, the argument is always correct. For each digit, the possible outcomes are 0,1,...,9, so the generating function for each digit is $1 + x + x^2 + \dots + x^9$. Since you are asking for the number of possible strings consisting of $L$ digits and summing up to a given number $t$, the answer is precisely the coefficient of $x^t$ in the product of these $L$ generating functions. | |
| Feb 18, 2011 at 16:12 | comment | added | mna | I am willing to believe you, but does your argument still hold after examining past the first 10 numbers in the sequence, when the summation starts to be used? I added a latex that I think is the closed form. | |
| Feb 18, 2011 at 10:45 | history | answered | Tom De Medts | CC BY-SA 2.5 |