Intereting Posts

Is the function $ f(x,y)=xy/(x^{2}+y^{2})$ where f(0,0) is defined to be 0 continuous?
Without appealing to choice, can we prove that if $X$ is well-orderable, then so too is $2^X$?
Strictly increasing function with $f'(x) = f(f(x))$
Is is possible to obtain exactly 16 black cells?
Instructive proofs in functional analysis
Intuitive explanation of binomial coefficient
Proof for Dirichlet Function and discontinuous
Axioms for sets of numbers
Difference between logarithm of an expectation value and expectation value of a logarithm
(non)equivalence of definition of non-atomic measure for finitely additive measure
If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?
Continuous Collatz Conjecture
Convergence of test-functions is not induced by any metric.
How is the codomain for a function defined?
Localization of a prime ideal in $\mathbb{Z}/6\mathbb{Z}$

How many ways are there to stack coins on top of the other (2D stack) without any coin falling down ?

Here’s an example for $n=3$:

- Catalan number - combinatoric
- How to deal with this double summation?
- Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?
- Catalan's constant and $\int_{0}^{2 \pi} \int_{0}^{2 \pi} \ln(\cos^{2} \theta + \cos^{2} \phi) ~d \theta~ d \phi$
- Simplifying Catalan number recurrence relation
- Catalan Numbers Staircase bijection

Now this is most likely just like the monotonic path of Catalan number with up and down instead of up and right but I just don’t get why is that ? Well, any advice would be appreciated.

- Probability of having $k$ empty urns after putting $n$ balls into $n$ urns
- Probability of rolling a dice 8 times before all numbers are shown.
- How many solutions are there to $x_1 + x_2 + … + x_5 = 21$?
- What's the chance of an explicit series of integers in a limited random distribution?
- Number of strings lenght $n$ with no consecutive zeros
- arrangement of the word $“\bf{MATHEMATICS}”$ in which no two same letter occur together.
- In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other?
- Are these numbers $h_{r,s}$ irrational?
- How much space do I need to sort my socks?
- number of combinations without repetition with limited supply

A picture is worth a thousand words, they say:

- Finding $a_n$ for very large $n$ where $a_n = a_{n-1} + a_{n-2} + a_{n-3} + 2^{n-3} $
- Is $\log(z^2)=2\log(z)$ if $\text{Log}(z_1 z_2)\ne \text{Log}(z_1)+\text{Log}(z_2)$?
- Help with this trigonometry problem
- Two circles overlap?
- Does the likelihood of an event increase with the number of times it does not occur?
- Convergence in $L^p$ and convergence almost everywhere
- Convex combination of projection operators
- Prove the inequality involving multiple integrals
- Legendre transform of a norm
- Can this intuition give a proof that an isometry $f:X \to X$ is surjective for compact metric space $X$?
- Is there an infinite connected topological space such that every space obtained by removing one point from it is totally disconnected?
- Is there a bijection from to R?
- Is such a map always null-homotopic?
- A question on the proof of 14 distinct sets can be formed by complementation and closure
- the diameter of nested compact sequence