Poset associahedra
Abstract
For each poset $P$, we construct a polytope $A(P)$ called the $P$associahedron. Similarly to the case of graph associahedra, the faces of $A(P)$ correspond to certain tubings of $P$. The Stasheff associahedron is a compactification of the configuration space of $n$ points on a line, and we recover $A(P)$ as an analogous compactification of the space of orderpreserving maps $P\to\mathbb{R}$. Motivated by the study of totally nonnegative critical varieties in the Grassmannian, we introduce affine poset cyclohedra and realize these polytopes as compactifications of configuration spaces of $n$ points on a circle. For particular choices of (affine) posets, we obtain associahedra, cyclohedra, permutohedra, and type B permutohedra as special cases.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07257
 Bibcode:
 2021arXiv211007257G
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Geometric Topology;
 Primary: 52B11. Secondary: 05E99;
 06A07;
 54D35
 EPrint:
 30 pages, 10 figures