MathOverflow

Often, one deals with objects that can have a certain multiplicity attached to it. In the case of graphs, the multiplicity of vertices connected by an edge gives rise to a hypergraph. Now, in set theory, the axioms are usually stated for sets, and not...

Let $k$ be a positive integer. Let $n$ and $m$ be positive integers with $m$ roughly $\log_2 n$, let $V$ be an $n$-dimensional vector space over $\mathbb{F}_2$, let $W$ be an $m$-dimensional vector space over $\mathbb{F}_2$, where $\mathbb{F}_2$ is the...

Is there a topology textbook with a copyleft license?
Postscript.
You may check my notes now.

Let
$T(n,k)$ be an unique coefficients (represented as an irregular triangle) such that for all $n,m \in \mathbb{N}$ we have $$ \sum\limits_{k=1}^{2n} 2^{k-1} \binom{m+k}{k} T(n,k) = (m+2)^{2n} - 1. $$
I conjecture that $$ \sum\limits_{k=1}^{2n} T(n,k) = 2. $$ More precisely, I conjecture that $$ \sum\limits_{k=3}^{2n} T(n,k) = 0. $$ I also conjecture that $T(n,k)$ are integer coefficients for all $1 \leqslant k \leqslant 2n$ iff $2n$ is a power of...