User D Poole

31 votes

Accepted

Which is the explanation of the identity $\sum_{k=0}^n {n \choose k}k^2 = 2^{n-2}n(n+1)$?

answered Jun 3, 2016 at 20:37

17 votes

Examples of problems that are easier in the infinite case than in the finite case.

answered Aug 12, 2016 at 19:17

16 votes

Exact probability of random graph being connected

answered Dec 5, 2013 at 22:16

13 votes

Expectation number of cycles in a Erdős–Rényi random directed graph $G(n,p)$

answered Mar 26, 2014 at 13:03

6 votes

Accepted

black and white balls in the box

answered Jul 17, 2013 at 17:03

6 votes

Accepted

Prove $\lim_{n\to\infty} \frac{a_n}{n}$ exists for positive sequence where $a_{n+m} \leq a_n + a_m$

answered Jun 1, 2016 at 15:11

6 votes

Accepted

Combinatorial identity $\sum\limits_{k=0}^{n}\frac{n-k}{k+1}\binom{n}{k}^2 = \binom{2n}{n-1}$

answered Jun 20, 2016 at 19:02

5 votes

Accepted

Show $y = \sum_{k=1}^\infty \frac{k^{k-1}}{k!} x^k$ satisfies $ye^{-y} = x$.

answered Mar 6, 2017 at 17:01

5 votes

Accepted

Convergence of $\int_{-\infty}^{\infty} \sin p(x)\,dx$ where $p$ is a polynomial with $\deg p>1$

answered Aug 23, 2013 at 14:44

5 votes

Expected shortest path in random graph

answered Sep 28, 2013 at 1:28

4 votes

Accepted

How to compute the average number of wedges and triangles present in the Erdős-Rényi random graph?

answered Sep 18, 2014 at 0:35

4 votes

Minimum number of edges to ensure connectedness

answered Nov 24, 2014 at 16:09

4 votes

Is there an injection between $\mathbf{R}$ and $[0,1)$

answered Nov 18, 2014 at 0:13

3 votes

Accepted

probability of having cycle in a random directed graph with a given in-degree distribution

answered Nov 6, 2015 at 20:22

3 votes

Whether or not a certain function is measurable

answered Oct 16, 2014 at 0:33

3 votes

How many centers in a infinite connected graph?

answered Jun 27, 2013 at 15:21

3 votes

Accepted

Probability that binomial random graph is bipartite

answered Jun 27, 2013 at 18:46

3 votes

Accepted

Asymmetry of random graphs

answered Jun 1, 2014 at 17:14

3 votes

Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$

answered Aug 12, 2016 at 14:38

3 votes

Accepted

Does there exist a random variable $\xi$ and a constant $c \neq 0$ such that $\xi + c \stackrel{d}{=} \xi$?

answered Jun 24, 2016 at 17:16

3 votes

Which has higher variance, coin toss vs dice roll?

answered Jun 26, 2016 at 18:10

3 votes

Proof of $\sum\limits_{n=1}^{\infty} \frac{x^n \log(n!)}{n!} \sim x \log(x) e^x$ as $x \to \infty$

answered Dec 9, 2015 at 21:41

3 votes

Accepted

Threshold probabilities in Erdos-Renyi random graph model $G(n,p)$ and intermediate value theorem

answered May 23, 2016 at 14:08

2 votes

Accepted

Replacing initial probability in $G(n,\frac{1}{2})$ with $G(n,\frac{1}{3})$ for not appearance edges

answered May 25, 2016 at 17:23

2 votes

Accepted

On the number of some special components of a graph

answered May 18, 2016 at 18:46

2 votes

Limit probability of a complete bipartite random graph $G(n,n,p)$ is connected

answered May 20, 2016 at 18:00

2 votes

Accepted

A non-negative measurable function is a sum of the averages of some characteristic functions

answered Dec 11, 2015 at 19:52

2 votes

Prove that $2^n$ does not divide $n!$

answered Jun 1, 2016 at 18:30

2 votes

Accepted

A Closed Form Lower Bound Approximating $p_{n,m,s} = n![z^n]\left(\sum_{k=0}^s\frac{z^k}{k!}\right)^m$

answered Jul 5, 2016 at 14:31

2 votes

Accepted

Probability that at least 2 edges of $\Gamma_{n,N}$ shall have a point in common

answered Jun 17, 2016 at 12:34

Stack Exchange Network

70 Answers

Which is the explanation of the identity $\sum_{k=0}^n {n \choose k}k^2 = 2^{n-2}n(n+1)$?

Examples of problems that are easier in the infinite case than in the finite case.

Exact probability of random graph being connected

Expectation number of cycles in a Erdős–Rényi random directed graph $G(n,p)$

black and white balls in the box

Prove $\lim_{n\to\infty} \frac{a_n}{n}$ exists for positive sequence where $a_{n+m} \leq a_n + a_m$

Combinatorial identity $\sum\limits_{k=0}^{n}\frac{n-k}{k+1}\binom{n}{k}^2 = \binom{2n}{n-1}$

Show $y = \sum_{k=1}^\infty \frac{k^{k-1}}{k!} x^k$ satisfies $ye^{-y} = x$.

Convergence of $\int_{-\infty}^{\infty} \sin p(x)\,dx$ where $p$ is a polynomial with $\deg p>1$

Expected shortest path in random graph

How to compute the average number of wedges and triangles present in the Erdős-Rényi random graph?

Minimum number of edges to ensure connectedness

Is there an injection between $\mathbf{R}$ and $[0,1)$

probability of having cycle in a random directed graph with a given in-degree distribution

Whether or not a certain function is measurable

How many centers in a infinite connected graph?

Probability that binomial random graph is bipartite

Asymmetry of random graphs

Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$

Does there exist a random variable $\xi$ and a constant $c \neq 0$ such that $\xi + c \stackrel{d}{=} \xi$?

Which has higher variance, coin toss vs dice roll?

Proof of $\sum\limits_{n=1}^{\infty} \frac{x^n \log(n!)}{n!} \sim x \log(x) e^x$ as $x \to \infty$

Threshold probabilities in Erdos-Renyi random graph model $G(n,p)$ and intermediate value theorem

Replacing initial probability in $G(n,\frac{1}{2})$ with $G(n,\frac{1}{3})$ for not appearance edges

On the number of some special components of a graph

Limit probability of a complete bipartite random graph $G(n,n,p)$ is connected

A non-negative measurable function is a sum of the averages of some characteristic functions

Prove that $2^n$ does not divide $n!$

A Closed Form Lower Bound Approximating $p_{n,m,s} = n![z^n]\left(\sum_{k=0}^s\frac{z^k}{k!}\right)^m$

Probability that at least 2 edges of $\Gamma_{n,N}$ shall have a point in common