Intereting Posts

A question concerning a set connected to a sequence of measurable functions
Transforming integral equation to differential equation
Are there vector bundles that are not locally trivial?
Calculating the determinant gives $(a^2+b^2+c^2+d^2)^2$?
A probability question that I failed to answer in a job interview
Definition of semi-ring homomorphism
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
Does this sequence have any mathematical significance?
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
The final number after $999$ operations.
Limits and convolution
Are these numbers $h_{r,s}$ irrational?
Stochastic Integrals are confusing me; Please explain how to compute $\int W_sdW_s$ for example
Formula for the summation of this sequence?

How many ways are there to tile an $n\times n$ square with exactly $n$ rectangles, each of which has integer sides and area $n$?

The sequence $C(n)$ begins 1, 2, 2, 9, 2, 46, 2, 250, 37. Clearly $C(p) = 2$ for prime $p$. The value $C(8) = 250$ was provided to me by Sjoerd Visscher, but I cannot vouch for it personally, not having seen the details of his enumeration.

OEIS was no help.

- How to calculate the expected value when betting on which pairings will be selected
- Roots of maps of finite sets
- Limit of alternating sum with binomial coefficient
- Number of cyclic paths in a rectangular grid?
- Dense board with sparse rook attacking
- in a mountain climbing expeditions 5 men and 7 women are to walk

- How many ways are there to arrange the letters in the word “mississippi” such that all “p” precede all “i”?
- Expected number of people sitting in the right seats.
- Number of non decreasing sequences of length $M$
- Why is a circle in a plane surrounded by 6 other circles?
- Number of ways to choose 6 objects when they are of 11 different kinds
- A closed form for $T_N = 1 + \sum\limits_{k=0}^{N-2}{(N-1-k)T_k}$?
- Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
- What is an intuitive explanation of the combinations formula?
- Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
- counting full bipartite matchings

Sorry to poke a dead post but it was near the top of the “unanswered questions” queue for me and it’s a decent problem.

Working locally should provide a good avenue of attack on this problem.

For instance, a relatively straightforward analysis (which I’ll post if there is interest) yields:

$$ C(p^2) = 2\left(\sum_{k=0}^{p} {p^2-k(p-1) \choose k}\right)-1 $$

- Find the expected number of two consecutive 1's in a random binary string
- How do I solve $\lim_{x\to1}\frac{\sqrt{2-x}-1}{1+\sqrt{x-2}}$?
- Find the point in a triangle minimizing the sum of distances to the vertices
- How do solve this integral $\int_{-1}^1\frac{1}{\sqrt{1-x^2}}\arctan\frac{11-6\,x}{4\,\sqrt{21}}\mathrm dx$?
- Does weak completeness (“If $\vDash\phi$, then $\vdash\phi$”) imply strong completeness (“If $\Gamma\vDash\phi$, then $\Gamma\vdash\phi$”)?
- Convex combination of projection operators
- Curvature of planar implicit curves
- Solving Cubic Equations (With Origami)
- How to model mutual independence in Bayesian Networks?
- If $(a,b)=1$ then prove $(a+b, ab)=1$.
- Bound of sequence
- Integral $\int_0^1\frac{1-x^2+\left(1+x^2\right)\ln x}{\left(x+x^2\right)\ln^3x}dx$
- Linear algebra on Fibonacci number
- Sum and product of Martingale processes
- How to show that the extended code of cyclic binary hamming code can fix single and two adjacent positions errors?