3 problems

Let $\Delta$ be the face complex of an $n$-gon. A binary geometry for $\Delta$ is a binary geometry whose underlying flag complex is $\Delta$. Binary geometry existence conjecture.…

Let $I$ and $J$ be sets indexing the $u$-variables of $\mathscr{P}_n$, and let $h_{I,n}$ denote the correction term in the equation for $u_I$. Compatibility-degree and positivity c…

Let $\mathscr{P}_n$ be the generalized permutohedron with variables $u_I$ indexed by the relevant sets $I$. For sets $I$ and $J$, write $J||I$ for their positive integer compatibil…