Intereting Posts

Proving that if $A^n = 0$, then $I – A$ is invertible and $(I – A)^{-1} = I + A + \cdots + A^{n-1}$
Dice Roll Cumulative Sum
Why can we modify expressions to use limits?
Evaluate $ \sum\limits_{n=1}^{\infty}\frac{n}{n^{4}+n^{2}+1}$
Uniformization theorem and metrics on Riemann surfaces
Asymptotic behavior of Harmonic-like series $\sum_{n=1}^{k} \psi(n) \psi'(n) – (\ln k)^2/2$ as $k \to \infty$
Help with a proof. Countable sets.
Normality is not hereditary
Books with similar coverage to Linear Algebra Done Wrong
Probability distribution for the perimeter and area of triangle with fixed circumscribed radius
What happens to the PDE if resistive force equals $av^2$ instead of $av$?
What does “X% faster” mean?
Topological vector space with discrete topology is the zero space
How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes?
Folland, Real Analysis problem 1.18

How many possible shapes can one make by rearranging $n$ square shaped blocks, with and without allowing rotational symmetry? For example, for $n = 4$, there are seven possible shapes after discounting rotational symmetry, as in Tetris.

How does this number change if one of the blocks is coloured – distinguishable from the rest? For instance, for $n = 2$ there are only two shapes one can make (with rotational symmetry admissible). However, if one block is coloured, one can make four shapes, with the second block left, right, above and below the coloured block.

- Can an 8×8 square be tiled with these smaller squares?
- Coloring $\mathbb R^n$ with $n$ colors always gives us a color with all distances.
- Scalene rectangulation of a square: let me count the ways
- Maximum number of acute triangles
- Shooting Game for Fun
- Maximum distance between points in a triangle

- What is the proof that the total number of subsets of a set is $2^n$?
- What tactics could help with this probability questions
- Verify that R(p,2) = R(2,p) = p, where R is the Ramsey number
- Combinatorial proof that binomial coefficients are given by alternating sums of squares?
- $K_{1,3}$ packing in a triangulated planar graph
- Non-probabilistic proofs of a binomial coefficient identity from a probability question
- Generate Random Latin Squares
- A Combinatorial Proof of Dixon's Identity
- Why is a general formula for Kostka numbers “unlikely” to exist?
- Proving identity $ \binom{n}{k} = (-1)^k \binom{k-n-1}{k} $. How to interpret factorials and binomial coefficients with negative integers.

There has been much work done on polyominoes. The number counting rotations and reflections as the same is given in OEIS A000105. Counting reflections as distinct but rotations as the same gives A00988

- Product of two cyclic groups is cyclic iff their orders are co-prime
- Closed form of $\int_0^1(\ln(1-x)\ln(1+x)\ln(x))^2\,dx$
- $D(G)$ is finite if $G$ has finitely many commutators
- separable iff homeomorphic to totally bounded
- Linear Independence of an infinite set .
- Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt {n!}}$
- Pedagogy: How to cure students of the “law of universal linearity”?
- basis of a vector space
- If both integers $x$ and $y$ can be represented as $a^2 + b^2 + 4ab$, prove that $xy$ can also be represented like this …
- universal property in quotient topology
- I need to calculate $x^{50}$
- Proving that for infinite $\kappa$, $|^\lambda|=\kappa^\lambda$
- If $|a| = 12, |b| = 22$ and $\langle a \rangle\cap \langle b\rangle \ne e$, prove that $a^6 = b^{11}$
- The group of $k$-automorphisms of $k]$, $k$ is a field
- Is $z^{-1}(e^z-1)$ surjective?