Permuto-associahedra as deformations of nested permutohedra
- Fu Liu (University of California, Davis, Davis, USA)
A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset (with a reasonable structure), determine whether there exists a polytope whose face lattice it the poset. In 1990s, Kapranov defined a poset called permuto-associhedron as a hybrid between the face poset of the permutohedron and the associahedron, and he asked whether this poset is realizable. Shortly after his question was posed, Reiner and Ziegler provided a realization. In this talk, I will discuss a different construction we obtained as a deformations of nested permutohedra.