New posts in combinatorics

One-Line Proof for $n! \geq (\frac n e)^n$

combinatorics inequality factorial

Help with combinatorial proof of identity: $\sum_{k=1}^{n} \frac{(-1)^{k+1}}{k} \binom{n}{k} = \sum_{k=1}^{n} \frac{1}{k}$

sequences-and-series combinatorics discrete-mathematics binomial-coefficients combinatorial-proofs

Number of triangles sharing all vertices but no sides with a given octagon

Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

combinatorics summation generating-functions closed-form

Number of spanning trees in a ladder graph

combinatorics graph-theory trees

Non-crossing partitions without singletons

combinatorics recurrence-relations combinatorial-proofs catalan-numbers

How many rectangles with the dark dot are there?

Number of total possibilities for an equation

combinatorics discrete-mathematics

How are inclusion-wise maximal and minimal sets defined?

combinatorics matroids

Probability of $13$ men and $2$ women divided in $3$ equal groups such that no women are in same group

probability combinatorics solution-verification permutations

Good upper bound for $\sum\limits_{i=1}^{k}{n \choose i}$?

combinatorics discrete-mathematics binomial-coefficients asymptotics

Solving the recurrence relation $A_n=n!+\sum_{i=1}^n{n\choose i}A_{n-i}$

combinatorics recurrence-relations

Finding coefficient of generating function

combinatorics generating-functions

In how many ways can 1500 be resolved into two factors?

combinatorics elementary-number-theory

Why isn't there only one way of painting these horses?

combinatorics multinomial-coefficients

Probability of a Full House for five-card hand.

probability combinatorics card-games poker

Number of surjections between finite sets (what is wrong with my solution?)

probability combinatorics elementary-set-theory solution-verification

Can you win the monochromatic urn game?

combinatorics graph-theory computational-complexity combinatorial-game-theory matching-theory

Polynomial expansion of a product, and Stirling numbers?

Given $2n$ points in the plane, $n$ blue points and $n$ red points, no $3$ are collinear. Prove that we have at least two "balanced lines".

combinatorics geometry puzzle