Intereting Posts

The boundary of union is the union of boundaries when the sets have disjoint closures
Proving that any rational number can be represented as the sum of the cubes of three rational numbers
$\frac{1}{\sin 8^\circ}+\frac{1}{\sin 16^\circ}+…+\frac{1}{\sin 4096^\circ}+\frac{1}{\sin 8192^\circ}=\frac{1}{\sin \alpha}$,find $\alpha$
Solving $\sin\theta -1=\cos\theta $
Prime Appearances in Fibonacci Number Factorizations
Finding the Number of Positive integers such that $\lfloor{\sqrt{n}\rfloor} \mid n$
Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals
Is zero odd or even?
Why non-measurable sets exist?
In $\ell^1$ but not in $\ell^2$?
Extending a homomorphism of a ring to an algebraically closed field
Checking a fundamental unit of a real quadratic field
One-to-one function from the interval $$ to $\mathbb{R}\setminus\mathbb{Q}$?
Best representation of a polynomial as a linear combination of binomial coefficients
Is a least squares solution to $Ax=b$ necessarily unique

There is a strong relationship between (rooted) trees and hierarchically clustered graphs as can be seen here:

The tree – consisting of circles (green = the root, blue, red, black = the leaves) and thin lines – can be seen as the result of a hierarchical cluster analysis of the graph consisting of the black circles and thick lines. Hierarchically clustered graphs can be defined as those graphs for which an appropriately defined hierarchical cluster analysis yields a (non-trivial) tree.

- Can anyone clarify how a diverging sequence can have cluster points?
- Stationary distribution for directed graph

Trees are very elegantly defined and characterized as graphs that are connected and have no cycles. But how can their companions – the hierarchically clustered graphs – be characterized in a similar elegant way, or characterized at all (next to their definition above)?

- Minimal time gossip problem
- Motivation for spectral graph theory.
- Prove that the tesseract graph is non-planar
- Prove that every undirected finite graph with vertex degree of at least 2 has a cycle
- eigen decomposition of an interesting matrix
- How can this technique be applied to a different problem?
- A closed Knight's Tour does not exist on some chessboards
- Finding characteristic polynomial of adjacency matrix
- Is there exists a $k$-iso-regular ($k \ge 3$) non-planar graph of degree at most three?
- How many ways can one paint the edges of a Petersen graph black or white?

- Sum(Partition(Binary String)) = $2^k$
- No difference between $0/0$ and $0^0$?
- Is $f(x)=1/x$ continuous on $(0,\infty)$?
- Limit of the difference quotient of $f(x) = \frac{2}{x^2}$, as $x\rightarrow x_0$
- Riemannian Manifolds with $n(n+1)/2$ dimensional symmetry group
- Density of Gaussian Random variable conditioned on sum
- The graph of the function $f(x)= \left\{ \frac{1}{2 x} \right\}- \frac{1}{2}\left\{ \frac{1}{x} \right\} $ for $0<x<1$
- Is there an analytic solution for the equation $\log_{2}{x}+\log_{3}{x}+\log_{4}{x}=1$?
- convex function in open interval is continuous
- Is there any uncountably infinite set that does not generate the reals?
- How does the existence of a limit imply that a function is uniformly continuous
- Find all conditions for $x$ that the equation $1\pm 2 \pm 3 \pm 4 \pm \dots \pm n=x$ has a solution.
- On the density of $C$ in the space $L^{\infty}$
- Why are maximal ideals prime?
- The matrix specify an algernating $k$-tensor on $V$, and dim$\bigwedge^k(V^*)=1$