All Questions

From "Noncrossing partitions in surprising locations" by Jon McCammond: Certain mathematical structures make a habit of reoccuring in the most diverse list of settings. Some obvious ...

Looking for references for one or more of the following four sets of partition polynomials 1a) through 4a), particularly those which present geometric / topological combinatorial interpretations. ...

For $n\in \mathbb{N}$ let $B_n$ be the linear operator taking a function $f$ on the unit interval $I=[0,1]$ to its $n$-th Bernstein polynomial $B_nf$, $$ B_nf(x):=\sum_{k=0}^n\binom{n}{k} f\Big(\...

Let $f(x)=\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$, where $u\in\mathbb{Z}^+$ and $\binom{x}{l}=\frac{x(x-1)\dots(x-l+1)}{l!}$ for all $l\in\mathbb{Z}^+$. Then can we prove $f(x)$ is a convex ...

In answering another MathOverflow question, I stumbled across the sequence of polynomials $Q_n(p)$ defined by the recurrence $$Q_n(p) = 1-\sum_{k=2}^{n-1} \binom{n-2}{k-2}(1-p)^{k(n-k)}Q_k(p).$$ Thus: ...