3 problems

Let $P$ be a simplicial polytope, and let $\widehat{\gamma}(P)=(\widehat{\gamma}_0(P),\widehat{\gamma}_1(P),\dots,\widehat{\gamma}_d(P))$ be its gamma-vector with respect to the st…

Let $n\in\mathbb{N}$ and $k\in\{1,\ldots,n\}$. Let $\beta>(n-1)/2$ be an integer or half-integer, and let $\tilde{\mathbb{J}}_{n,k}(\beta)$ denote the corresponding dual expected i…

Let $\beta\geq -1$ be an integer or half-integer, and let $n\in\mathbb{N}$ and $k\in\{1,\ldots,n\}$. The quantity $\mathbb{J}_{n,k}(\beta)$ denotes the expected internal-angle sum…