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  • 132 votes cast
Oct
23
asked A confusing contradiction in Menger's theorem
Oct
13
accepted Is there any easier way to get the asymptotic value of this sum?
Oct
13
asked Is there any easier way to get the asymptotic value of this sum?
Oct
12
comment What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
I did computer simulation and $S(n)$ indeed goes to $1/2 log(n)$. But I am afraid your proof is a difficult for me to understand. Is there any other simpler proofs?
Oct
10
accepted Does this sum go to 0?
Oct
10
accepted Given a random graph $G_{n,p}$, how to get the expectation of number of components with $k$ vertices and $k$ edges?
Oct
10
comment Does this sum go to 0?
Of course I could be wrong. It indeed might not go to 0. But that means I wasted another half a day on this problem.
Oct
10
comment Does this sum go to 0?
@process91, think about this sum, $\sum_{k=1}^{\lceil n/2 \rceil} (1-p)^{k(n-k)}$. Erdos has proved it goes to 0, if $p = c \log n / n, c > 1$. I'm actually trying to mimic what he did : renyi.hu/~p_erdos/1961-15.pdf
Oct
10
comment Does this sum go to 0?
I'm taking a course of random graph. The exercises are really difficult. Sometimes no students in class could solve all of them. These equations are the best I can reach. If I can get $S \to 0$ then I'm done. But I've completely no idea if this is the correct direction or it's a just another dead end.
Oct
10
asked Does this sum go to 0?
Oct
10
accepted What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$?
Oct
10
comment What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$?
Oh yeah, I should be more careful about typos.
Oct
10
revised What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$?
edited body
Oct
10
asked What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$?
Oct
10
comment What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
That's really impressive.
Oct
10
accepted What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
Oct
10
comment What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
The 2 $(n-2)$ is a typo, I just fixed it.
Oct
10
revised What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
edited body
Oct
10
asked What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$?
Oct
8
revised Given a random graph $G_{n,p}$, how to get the expectation of number of components with $k$ vertices and $k$ edges?
edited title