2 problems

Stanley's conjectures. The polynomial $\ell_V(\Gamma,x)$ has unimodal coefficients for every simplicial subdivision $\Gamma$ of $2^V$, and, for every flag simplicial subdivision, t…

For a permutation $\sigma\in S_n$, let $\operatorname{inv}(\sigma)$ and $\operatorname{exc}(\sigma)$ denote its inversion number and excedance number, respectively, and define … Th…