8 problems

Let $P$ be a naturally labeled, graded poset with nonnegative rank function $\rho$, and set ${\boldsymbol s}=\rho+1$. Let $O(P,{\boldsymbol s})$ denote the corresponding…

Let ${\boldsymbol s}\in\mathbb{Z}_{\geq 1}^n$ be a sequence. Suppose there exists ${\boldsymbol c}\in\mathbb{Z}^n$ such that … for every $j>1$, with $c_1=1$. Kohl–Olsen's levelness…

Let ${\boldsymbol s}\in\mathbb{Z}_{\geq 1}^n$ be given, and let $\mathbf{P}_n^{({\boldsymbol s})}$ denote the corresponding ${\boldsymbol s}$-lecture hall simplex. Hibi–Tsuchiya–Ol…

Let ${\boldsymbol s}\in\mathbb{Z}_{\geq 1}^n$ be a sequence, and let $\mathbf{P}_n^{({\boldsymbol s})}$ denote the corresponding $s$-lecture hall polytope. Levelness conjecture. Su…

Let ${\boldsymbol s}=(s_1,s_2,\ldots,s_n)$ be any sequence, and let $\overleftarrow{\boldsymbol s}$ denote its reverse. Let $\mathbf{P}_n^{({\boldsymbol s})}$ be the corresponding…

Let $P$ be a naturally labeled ranked poset, let $\rho$ be its rank function, and set $s=\rho+1$. The associated lecture hall polytope is $O(P,s)$. Regular unimodular triangulation…

Let $\boldsymbol{s}=(s_1,\ldots,s_d)$ be an integer sequence, and let $P_d^{(\boldsymbol{s})}$ denote the lecture hall polytope associated to $\boldsymbol{s}$. A triangulation is u…

Let $\boldsymbol{s}=(s_1,\ldots,s_d)$ be an integer sequence, and let $P_d^{(\boldsymbol{s})}$ denote the lecture hall polytope associated to $\boldsymbol{s}$. A lattice polytope i…