All Questions

Define the associahedra partition polynomial $$ \begin{split} A(x) &= 1 + A_1(u_1) z + A_2(u_1,u_2) z^2 + A_3(u_1,u_2,u_3) z^3 + \cdots\\ & \qquad\qquad = 1 + \sum_{n \geq 1} A_n(u_1,...,u_n) ...

The coefficients of the monomials $u_1^{e_1}u_2^{e_2} \ldots u_n^{e_n}$ of the partition polynomials (ParPs) $[M=M1]$ on pg. 831 of The Handbook of Mathematical Functions by Abramowitz and Stegun are ...

Suppose $R$ is a commutative Noetherian ring. Let $\mathcal{P}(R)$ be the poset of ideals of $R$ ordered by inclusion, and let $\Delta(R)$ be the order complex of $\mathcal{P}(R)$. $\Delta(R)$ is a ...

The integral face ring of a (finite) simplicial complex $K$ on $m$ vertices is the quotient ring $$\mathbb{Z}[K]=\mathbb{Z}[v_1,...,v_m]/\mathcal{I}_K$$ where $\mathcal{I}_K$ is the ideal generated by ...

Here was a question about resonance arrangement. It is defined as follows. Let $x_i$ be the standard coordinates on $\mathbb{C}^n$. For each nonempty $I\subseteq\{1,\dots,n\}$, define the hyperplane $...

The f-polynomials, $F_n(x)$ (cf. OEIS A126216, A033282, and A086810), and the h-polynomials, $H_n(x)$ (cf. A001263, the Narayana polynomials), of the family of simple convex polytopes the associahedra ...