3 problems

Let $M$ be a matroid. A pinned broken line shelling order is a shelling order obtained from a broken-line shelling whose normal vectors lie in the normal cone of one fixed vertex o…

Let $(1,h_1,\dotsc,h_e)$ be a sequence of natural numbers, and fix an index $i$. Suppose that for some positive integer $\alpha$, both … and … are pure $O$-sequences. Interval conj…

Let $h=(1,h_1,\dotsc,h_e)$ and $h'=(1,h'_1,\dotsc,h'_{e-1})$ be pure $O$-sequences. For a vector $H=(1,H_1,H_2,\dots,H_t)$, write $\Delta H=(1,H_1-1,H_2-H_1,\dots,H_t-H_{t-1})$ for…