# 12月10日 牟麗麗 博士學術報告（數學與統計學院）

Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties,a natural way to generate a new class of polytopes is to take the intersection $\mathcal{P}=\mathcal{P}_1\cap\mathcal{P}_2$, where $\mathcal{P}_1\in X$, $\mathcal{P}_2\in Y$.Two basic questions then arise:

1) when $\mathcal{P}$ is integral and

2) whether $\mathcal{P}$ inherits the old type from $\mathcal{P}_1, \mathcal{P}_2$ or  has a new type,that is, whether $\mathcal{P}$ is unimodularly equivalent to a polytope in $X\cup Y$ or not.

In this talk, we focus on the families of order polytopes and chain polytopes.Following the above framework, we create a new class of polytopes which are named order-chain polytopes.When studying  their volumes, we discover a natural relation with Ehrenborg and Mahajan's results on maximizing descent statistics.

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