All Questions

Let $n$ be positive integer. Consider its integer partitions denoting as $(m_1,\cdots,m_k)$, where $m_1+\cdots+m_k=n$ and the order does not matter. We ignore the case of $(m_1,\cdots,m_k)=n$. I am ...

Firs of all I ask my question, then I explain how this question arises in my mind and lastly what I tried to solve it. QUESTION: Let $P_{n,N}(k)$ be the number of composition of an integer $k$ in $n$ ...

Given a linear diophantine equation $$x_1+\dots+x_n=m\leq nn'$$ how many solutions does it have with each $x_i\in[0,n']\cap\mathbb Z$? Looking for asymptotics that parametrizes well with both $n$ and $...