4 problems

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

Let $P$ be a finite graded bounded poset, and let $P$ be Cohen–Macaulay. Denote by the characteristic Chow polynomial of $P$ the polynomial associated with $P$ in the Chow-polynomi…