Removahedral同余与permutree同余
Removahedral congruences versus permutree congruences
AI总结：
本文研究removahedron构造在quotientopes中的应用，证明permutree扇是仅有的removahedron实现的商扇，且可由编织扇构造，并给出类型锥的完整描述。
摘要：
经典地，结合多面体（associahedron）被构造为removahedron，即通过删除排列多面体（permutahedron）的面描述中的不等式而得到。这种removahedral构造扩展到所有permutree多面体（permutreehedra），它们介于排列多面体、结合多面体和立方体之间。本文中，我们研究所有quotientopes（实现弱序的格商）的removahedra构造。一方面，我们观察到permutree扇是仅有的由removahedron实现的商扇。另一方面，我们证明任何permutree扇都可以由从编织扇（braid fan）的任何实现构造的removahedron实现。我们的结果最终导致对permutree扇的类型锥的完整描述。
英文摘要：
The associahedron is classically constructed as a removahedron, i.e. by deleting inequalities in the facet description of the permutahedron. This removahedral construction extends to all permutreehedra (which interpolate between the permutahedron, the associahedron and the cube). Here, we investigate removahedra constructions for all quotientopes (which realize the lattice quotients of the weak order). On the one hand, we observe that the permutree fans are the only quotient fans realized by a removahedron. On the other hand, we show that any permutree fan can be realized by a removahedron constructed from any realization of the braid fan. Our results finally lead to a complete description of the type cone of the permutree fans.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
