Intereting Posts

Sigma field generated by a random variable!
Prove that definitions of the limit superior are equivalent
Extension of uniformly continuous function
Vector space of infinite sequences in $\Bbb R$
Let $y=g(x)$ be the inverse of a bijective mapping $f:R\to R f(x)=3x^3+2x.$Then area bounded by the graph of $g(x),x-$ axis and the ordinate at $x=5$
application of strong vs weak law of large numbers
Is $6.12345678910111213141516171819202122\ldots$ transcendental?
Statistics: Why doesn't the probability of an accurate medical test equal the probability of you having disease?
Computing $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}+1\right)}{k^2 \Gamma \left(\frac{k}{2}+\frac{3}{2}\right)}$ in closed form
Evaluate $\int \cos^2\theta\space d\theta$ using complex numbers.
Product of manifolds & orientability
Fractional oblongs in unit square via the Paulhus packing technique
Proving a relation between inradius ,circumradius and exradii in a triangle
The form $xy+5=a(x+y)$ and its solutions with $x,y$ prime
Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$

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.

- square cake with raisins
- Rectangle with lattice points
- Prove that there are exactly $k$ pairs $(x,y)$ of rational numbers with $0\leq x,y<1$ for which both $ax+by,cx+dy$ are integers.
- Maximum area of triangle inside a convex polygon
- Positivity of the alternating sum associated to at most five subspaces
- minimum lines, maximum points

- Are all uncountable infinities greater than all countable infinities? Are some uncountable infinities greater than other uncountable infinities?
- Number of ways to put N items into K bins with at least 1 per bin?
- How many ways to arrange the flags?
- Probability of predicting, then throwing, a particular multiset for 5 dice.
- Combinatorics identity question
- How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$?
- Enumerate certain special configurations - combinatorics.
- Number of partial functions between two sets
- How many bracelets can be formed?
- How many planar arrangements of $n$ circles?

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

- Characteristic subgroups of a direct product of groups
- Find a example such $\frac{(x+y)^{x+y}(y+z)^{y+z}(x+z)^{x+z}}{x^{2x}y^{2y}z^{2z}}=2016$
- How to prove Cauchy-Schwarz integral inequality?
- Distribution of a transformed Brownian motion
- Properties of matrices changing with the parity of matrix dimension
- Prove that if $\int_{a}^{b} f(x)$ exists, $\delta >0 $ such that $|\sigma_1 -\sigma_2|<\epsilon$
- What makes the inside of a shape the inside?
- Congruence modulo p
- Resource request: history of and interconnections between math and physics
- Arithmetical proof of $\cfrac{1}{a+b}\binom{a+b}{a}$ is an integer when $(a,b)=1$
- Scalene rectangulation of a square: let me count the ways
- Localizations of quotients of polynomial rings (2) and Zariski tangent space
- Raising a partial function to the power of an ordinal
- eigenvalues and eigenvectors for rectangular matrices
- minimum possible value of a linear function of n variables