Intereting Posts

$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
Find a basis for a solution set of a linear system
What is the proof that covariance matrices are always semi-definite?
If $\sum a_n$ converges then $\sum (-1)^n \frac {a_n}{1+a_n^2}$ converges?
$f,g,h$ are polynomials. Show that…
Evans PDE p.308 Exercise 16 (2nd ed)
Existence of acyclic coverings for a given sheaf
For given $n\times n$ matrix $A$ singular matrix, prove that $\operatorname{rank}(\operatorname{adj}A) \leq 1$
$R$ has a subring isomorphic to $R$.
When is it possible to lift a function to its covering space?
Minimizing sum $\sum_{k=1}^n |x_k-a|$, $a=\text{median}_{k}(x_k)$
On the zeta sum $\sum_{n=1}^\infty$ and others
External measure invariant under unitary transformations
What is the $m$th derivative of $\log\left(1+\sum\limits_{k=1}^N n_kx^k\right)$ at $x=0$?
Closed-form of $\int_{a}^{b}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx$ for some $a<b$

Given a bicubic planar graph consisting of faces with degree $4$ and $6$, so called Barnette graphs.

We can show that there are exactly six squares.

Kundor and I found six types of arrangements of the six squares:

- three pairs of squares $(2+2+2)$
- two triples arranged in row $(\bar3+\bar3)$
- two triples arranged like a triangle $(3^\triangle+3^\triangle)$
- six isolated squares $(1+1+1+1+1+1)$
- two pairs and two isolated squares $(2+2+1+1)$
- one pair and four isolated squares $(2+1+1+1+1)$

Is there anything known if any of these arrangements can be proven to be Hamiltonian?

For example, “3. two triples arranged like a triangle” gives much less structural degrees of freedom compared to “4. six isolated squares”…

- Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$
- The use of any as opposed to every.
- The time complexity of finding a neighborhood graph provided an unordered adjacency matrix
- no cycles if and only if has $n-m$ connected components
- The marriage problem with the constraint that a particular boy has to find a wife.
- Is there is a way to construct a covering space of a wedge of two circles for a given normal subgroup

- Difference between a sub graph and induced sub graph.
- Euler's formula for triangle mesh
- Prove a graph Containing $2k$ odd vertices contains $k$ distinct trails
- Show that there's a minimum spanning tree if all edges have different costs
- How many cycles, $C_{4}$, does the graph $Q_{n}$ contain?
- Spanning Trees of the Complete Graph Avoiding a Given Tree
- Graph and Number theory
- For a Planar Graph, is it always possible to construct a set of cycle basis, with each and every edge Is shared by at most 2 cycle bases?
- Graph theory and tree company
- Stationary distribution of random walk on a graph

- A strange puzzle having two possible solutions
- Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)
- How to do a very long division: continued fraction for tan
- Percentage of primes among the natural numbers
- Compact operators, injectivity and closed range
- When is the closure of an intersection equal to the intersection of closures?
- Does the series $\sum_{n=1}^\infty (-1)^n \frac{\cos(\ln(n))}{\sqrt{n}}$ converge?
- Given integers $a \ge b > 0$ and a prime number $p$, prove that ${pa \choose pb} \equiv {a \choose b} \mod p$.
- $G$ conservative iff counit components are extremal epi.
- Sum the series $\sum_{n = 0}^{\infty} (-1)^{n}\{(2n + 1)^{7}\cosh((2n + 1)\pi\sqrt{3}/2)\}^{-1}$
- A question about the relationship between submodule and ideal
- Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
- Is the Lie Algebra of a connected abelian group abelian?
- Sum of a Sequence of Prime Powers $p^{2n}+p^{2n-1}+\cdots+p+1$ is a Perfect Square
- infinitely many units in $\mathbb{Z}$ for any $d>1$.