Warren Moors and Julia Novak in a paper entitled "Order matters when choosing sets" proved that if 1 < w < t < v are integers then $${{{v}\choose {w}}\choose {t}} > {{{v …

I believe this question is due to Erdős and Graham, and I think it is still open: does the base 3 expansion of $2^n$ avoid the digit 2 for infinitely many $n$? If we concaten …

I assume everyone here knows the 24-game -- given 4 numbers, combine them using +,-,x,/ and parentheses to form 24. An obvious generalization is to give $n$ integers ${a_,...,a_n}$ …

I am trying to find a good lower bound for chromatic number of one family of graphs. I'm curious what are the known lower bounds for chromatic number. There are two obvious: $\chi( …

In combinatorics, one can sometimes get an algorithmic proof, which loosely has the following form: -The proof moves through stages -An invariant is shown to hold by induction fr …

Let $2 \leq k \leq n - 2$. I need to prove that any collection of sub-sets of [n] such that 2 different of them have exactly k common elements, consists of at most $n$ sub-sets. T …

If $V_\lambda$, $V_\mu$ and $V_\nu$ are irreducible representations of $GL_n$, the Littlewood-Richardson coefficient $c_{\lambda\mu}^\nu$ denotes the multiplicity of $V_\nu$ in th …

This question is related to a previous question of mine: http://mathoverflow.net/questions/32966/determinacy-interchanging-the-roles-of-both-players Given any set A of sequences …

The question may be of little interest to most people here on MathOverflow, but after browsing a pile of books in combinatorics, I had to ask it somewhere: What are the most effic …

Consider the $d$-dimensional integer lattice, $Z^d$. Call two points in $Z^d$ "neighbors" if their Euclidean distance is 1 (i.e., if they differ by 1 on exactly one coordinate). …

Let $g(x) = \exp(f(x))$. Assuming numerical (or symbolic) values of $f(x), f'(x), f''(x), \ldots, f^{(n)}(x)$ are known, is there a way to compute $g'(x), g''(x), \ldots g^{(n)}(x) …

I got to thinking about this problem while sifting through the math puzzles for dinner thread. There's a fun puzzle by rgrig which asks the guests to prove that when they came to …

I have derived an explicit formula for the Euler zigzag numbers, the number of alternating permutations for n elements: $$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j} …

This problem arises while studying the complexity of algorithms and I am quite unfamiliar with the subject. Consider the set F of injective functions from {1..N} to {1..M} we can …

Recently I discussed an experiment with a friend. Assume we start a random experiment. At first there is an array with size 100 000, all set to 0. We calculate at each round a rand …