4 problems

Let a matroid be a nonempty simplicial complex satisfying the exchange property: whenever $F$ and $G$ are faces with $|F|<|G|$, some $x\in G\setminus F$ has $F\cup\{x\}$ as a face.…

Let $h=(1,h_1,\ldots,h_e)$ be the $h$-vector of a simplicial polytope. If $h$ is palindromic and unimodal, define its differential sequence by … An $O$-sequence is the Hilbert func…

Roberts' conjecture. The sequence $\left(O_d/O_{d-1}\right)_d$ is decreasing and converges, as $d$ increases, to a number strictly greater than $1$. Finite $O$-sequences are the…

Let $\Delta$ be a PS ear-decomposable simplicial complex, and let $h(\Delta)$ denote its $h$-vector. The PS ear-decomposability conjecture. The vector $h(\Delta)$ is a pure…