AI 中文总结
研究利用图乘法多面体为无环关联多面体定义并实现新的乘法多面体，还对其商进行了研究，最终得出偏序集序多面体的区间多面体，为结合运算组合学提供了新的多面体相关内容。
AI 中文摘要
两类多面体构成了结合运算的组合学基础。关联多面体和乘法多面体分别捕捉运算本身以及尊重该运算的态射中的信息。这些多面体最初由斯塔谢夫用于对同伦结合空间及其同伦同态进行建模。后来，松弛和弱高阶范畴将它们用作交换图的形状。最近，关联多面体已被推广到基于图的版本，进而推广到偏序集：无环关联多面体。在此，我们利用图乘法多面体为无环关联多面体定义并实现新的乘法多面体。我们还研究了它们的商，最后得出偏序集序多面体的区间多面体。
英文摘要
Two families of polytopes underlie the combinatorics of associative operations. Associahedra and multiplihedra respectively capture the information in the operation itself and in the morphisms that respect that operation. The first applications of these polytopes, from Stasheff, were for modeling homotopy associative spaces and their homotopy homomorphisms. Later, lax and weak higher categories used both as the shapes of commuting diagrams. More recently, the associahedra have been generalized to versions based on graphs, and then to acyclic versions based on posets: the acyclonestohedra. Meanwhile, the associated multiplihedra have also been generalized to graph associahedra and generalized permutohedra. Here we complete that picture: we use the graph multiplihedra to define and realize new acyclic poset multiplihedra for the acyclic poset associahedra. Quotients of these are also studied, concluding with the conjectured interval polytopes of the order polytopes of posets.
Comments31 pages
