Tagged Questions
1
vote
0answers
85 views
Question about ratios and combinatorics
In this question that I posted yesterday (11/15):
I am solving a programming puzzle that consists of finding all the possible ways to build a brick wall of $48$" $\times$ $10$" (width $\times$ height ...
6
votes
1answer
527 views
Equation about generating functions and subfactorial
Suppose $G_n(w)$ is a formal power series (really a probability generating function, see the following explanation) of variable $w$, try to solve out $G_n(w)$ for all $n\ge0$ from the ...
3
votes
1answer
63 views
How to solve a functional equation of the form $1-g(f(s))=m(1-g(s))$?
I have arrived to this equation in several contexts within branching processes. It arises from textbook exercises, so it must be solvable somehow. Here $f$ is a probability generating function which ...
0
votes
2answers
127 views
How to solve the following system?
I need to find the function c(k), knowing that
$$\sum_{k=0}^{\infty} \frac{c(k)}{k!}=1$$
$$\sum_{k=0}^{\infty} \frac{c(2k)}{(2k)!}=0$$
$$\sum_{k=0}^{\infty} \frac{c(2k+1)}{(2k+1)!}=1$$
...
