New posts in Combinatorial Proofs

Is there a story proof behind the combinatorial identity $(n-2k)\binom{n}{k} = n\left[ \binom{n-1}{k} - \binom{n-1}{k-1} \right]$?

The number of pairs $(m,n)$ of coprime positive integers that divide $k$ is $d(k^2)$, where $d$ is the divisor counting function.

Let $x^2=y^2=1$ and $xy\neq yx$. There are $\binom{2n}{n}$ expressions of length $2n$ in $x$ and $y$ that are equal to $1$.

Combinatoric interpretation of an equality between sums

Combinatorial proof of identity involving central binomial coefficients

Proof for $\sum_{k=1}^n k2^k \binom{2n-k-1}{n-1} = n\binom{2n}{n}$?

Prove that $\sum_{k=0}^{\lfloor (n-1)/2 \rfloor} (-1)^k {n+1 \choose k} {2n-2k-1 \choose n} =\frac{ n(n+1)}2 $

Generalised Pascal Triangle with two-periodic formula

A combinatorial proof of the identity $\sum\limits_{k=0}^nk^2 {n \choose k}^2 = n^2 {2n - 2 \choose n- 1}$

Proof for $\sum_{i=0}^n \frac{n \choose i}{{2n-1} \choose i} = 2$.