New posts in combinatorics

Prove the identity $ \sum\limits_{s=0}^{\infty}{p+s \choose s}{2p+m \choose 2p+2s} = 2^{m-1} \frac{2p+m}{m}{m+p-1 \choose p}$

combinatorics binomial-coefficients

Proof concerning Stirling numbers of the first kind

combinatorics stirling-numbers

Find the simple closed form of summation from $k=0$ to $N$

combinatorics discrete-mathematics

How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3?

combinatorics

How many functions are possible to create in this example?

combinatorics functions discrete-mathematics proof-verification relations

Counting non-isomorphic relations

combinatorics discrete-mathematics relations

Is there a shorter way to prove this?

linear-algebra combinatorics

Venn diagram with rectangles for $n > 3$

combinatorics discrete-mathematics combinatorial-geometry rectangles

Catalan numbers and triangulations

combinatorics triangulation catalan-numbers

Catalan numbers. Sequence of balanced parentheses.

combinatorics combinations catalan-numbers

Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!

combinatorics recreational-mathematics rubiks-cube

How would I figure out how many anagrams of mississippi don't contain the word psi?

combinatorics statistics discrete-mathematics permutations

Probabilities in choosing committees

combinatorics

Showing there exists a sequence that majorizes another

combinatorics algorithms contest-math

Number of factors of a big number

combinatorics factoring prime-factorization

Finding the number of subsets of a set such that an element divides the succeeding element.

combinatorics elementary-number-theory divisibility puzzle

Is there a nice way of expanding multinomials of the form $(1+x+\cdots+x^l)^n$?

probability combinatorics

Why is $\frac{1}{\sqrt 5}\left[\left(\frac{1+\sqrt 5}{2}\right)^n-\left(\frac{1-\sqrt 5}{2}\right)^n\right]$ an integer? [duplicate]

combinatorics number-theory elementary-number-theory

Find all cycles (faces) in a graph

combinatorics graph-theory

Pine tree shaped in binomial coefficients and a proving the formula derived from the shape

combinatorics summation binomial-coefficients