Intereting Posts

Is there a cubic spline interpolation with minimal curvature?
Isolated vertex probabilities for different random graphs
Derangements with repetitive numbers
Given a torsion $R$-module $A$ where $R$ is an integral domain, $\mathrm{Tor}_n^R(A,B)$ is also torsion.
Prove: bounded derivative if and only if uniform continuity
Integrate $\int_{0}^{2\pi} \frac{R^{2}-r^{2}}{R^{2}-2Rr\cos \theta +r^{2}} d\theta= 2\pi$, by deformation theorem
On the number of Sylow subgroups in Symmetric Group
Is there a formula for sine and cosine?
Why is this formula for $(2m-1)!!$ correct?
Eigenvalues of a Random Matrix
Intuitive understanding of why the sum of nth roots of unity is $0$
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
Does perfectly normal $\implies$ normal?
When the roulette has hit 5 reds why shouldn't I bet to black?
Is there a counterpart of a base of a topology for a $\sigma$-algebra?

What is the **maximum** number of points that can be chosen from an $N$ by $N$ grid such that no $4$ of the chosen points form a rectangle with sides parallel to the axes of the grid?

Equivalently, what is the minimum number of points chosen from an $N$ by $N$ grid to guarantee a rectangle?

What if we remove also rule out rectangles with sides not parallel to the axes of the grid?

- Squaring the plane, with consecutive integer squares. And a related arrangement
- Can Three Equilateral Triangles with Sidelength $s$ Cover A Unit Square?
- An Olympiad Problem (tiling a rectangle with the L-tetromino)
- Coloring $\mathbb R^n$ with $n$ colors always gives us a color with all distances.
- Strictly convex sets
- Covering all the edges of a hypercube?

- If $|A|=30$ and $|B|=20$, find the number of surjective functions $f:A \to B$.
- Taking Seats on a Plane
- How many arrangements of $\{a,2b,3c,4d, 5e\}$ have no identical consecutive letters?
- Probability event with $70$% success rate occurs three consecutive times for sample size $n$
- Counting the number of permutations of a binary multiset that have >=1 partitions all ones?
- A game with two dice
- integer as sum of three binomials
- Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q^n}$?
- Is $\sum_{k=0}^{r}\binom{r}{k}(r-k-1)^{r-k}(k-1)^{k-1}+(r-2)^r=0$ right?
- Placing the integers $\{1,2,\ldots,n\}$ on a circle ( for $n>1$) in some special order

- Commutativity of special type of permutations
- Stirling number of the first kind: Proof of Recursion formula
- Exhibit an integral domain $R$ and a non-zero non-unit element of $R$ that is not a product of irreducibles.
- The set of real numbers and power set of the natural numbers
- Equivalence of definition for weak convergence
- Question about solvable groups
- Is there a consistent arithmetically definable extension of PA that proves its own consistency?
- Sobolev embedding for $W^{1,\infty}$？
- Functional equation $P(X)=P(1-X)$ for polynomials
- Cryptography textbook
- Tree having no vertex of degree 2 has more leaves than internal nodes
- Stability of periodic solution
- How to prove the next properties for Critical graph?
- Please help with differentiation under the integral
- A local-global problem concerning roots of polynomials