5 problems

Let $P$ be a simplicial poset, with associated polynomials $\operatorname{H}_{\widehat{P}}(x)$, $\operatorname{H}_{{\widehat{P}}^\ast}(x)$, and augmented polynomial…

Let $\mathrm{M}$ be a matroid, and let its Chow polynomial be the polynomial invariant associated with its lattice of flats. Ferroni–Schröter's conjecture. The Chow polynomial of…

Let $\mathcal{L}$ be a geometric lattice, let $a$ be an atom of $\mathcal{L}$, and let $\underline{\mathrm{H}}_{[a,\widehat{1}]}$ and $\mathrm{H}_{[a,\widehat{1}]}$ denote the augm…

Let $R_0=(\binom{n}{k})_{n,k=0}^{\infty}$, and let $\mathcal{A}_{R_0}$ be the associated Chow-Eulerian map. For a polynomial $f$, say that $f$ has a nonnegative expansion in the ba…

Let $P$ be a Cohen–Macaulay poset, with Chow polynomial $\operatorname{H}_{P}(x)$ and augmented Chow polynomial $\operatorname{H}^{\operatorname{aug}}_{P}(x)$. Interlacing conjectu…