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Feb
16
accepted $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points?
Feb
16
comment $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points?
Yes. Josh B. gave a clue in the comments. I forgot to calculate for $23,24$ points too.
Feb
16
comment $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points?
@JoshB. Oh, that is it then. I guess I forgot to count the rest of the points. $23,24$ points also result in a finalist.
Feb
16
asked $4$ judges must distribute grades from $1$ to $6$ for each participant. In how many ways one can score $22$ points?
Feb
16
asked Is it possible to represent any sequence as the coefficients of arbitrary generating functions?
Feb
16
asked What is the coefficient of $x^{10}$ in $\left[ \frac{1-x^3}{1-x}\right]\left[ \frac{1-x^4}{1-x}\right]\left[ \frac{1}{1-x}\right]^2$?
Feb
13
asked Doubts on the workings of generating functions?
Feb
13
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Who downvoted this?!
Feb
12
reviewed Approve Second Partial Derivative Test for a Three-Variable Function
Feb
12
comment Why to ignore the factorials as part of the coefficients in the exponential generating function?
Yes. You're assuming it's that way by definition. But for example, $0!=1$, people usually say that this is true because of definition, but it's actually defined that way because it yields desirable answers in a lot of concepts. The concept of factorial per se would break if $0!=0$ in $a\choose 0$, for example.
Feb
11
asked Why to ignore the factorials as part of the coefficients in the exponential generating function?
Feb
10
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Thanks for your answer. Could you clarify a little bit on your steps? Your answer seems really interesting, but it's not really clear what you are doing there: It seems that you're using techniques of analysis (some kind of treatment of series I never seen before). [Please, do not erase your answer because of my stupidity, leave it there and write a little bit on every step. Some day this answer might enhance my knowledge a lot].
Feb
9
accepted How to obtain the chromatic polynomial of $C_5$?
Feb
9
accepted What is the connection with $g=1+\frac{1}{g}$ and $G_n= 1+\frac{1}{G_{n-1}}$?
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
I don't understand how you go from $1$ to $2$ here.
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Oh, nevermind. I remember it: $\frac{(x-x^7)^4}{(1-x)^4}=(x-x^7)^4\times \frac{1}{(1-x)^4}=(x-x^7)^4\times (1-x)^{-4}$.
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
One silly thing: How does $\left[\frac{x-x^7}{1-x}\right]^4$ becomes $x^4(1-x^6)^4(1-x)^{-4}$?
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Why if the sum from $r=0$ make it become $\frac{x-x^7}{1-x}$?
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Excuse me, isn't it: $\displaystyle \sum_{r=1}^6 x^r=\frac{1-x^7}{1-x}$ ?
Feb
8
comment Find the number of ways to obtain a total of $15$ points by throwing $4$ different dice?
Great! Thank you very much.