$P$-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 nested collections of subsets 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 order-preserving 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 e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.07257
- arXiv:
- arXiv:2110.07257
- Bibcode:
- 2021arXiv211007257G
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Geometric Topology;
- Primary: 52B11. Secondary: 05E99;
- 06A07;
- 54D35
- E-Print:
- 30 pages, 10 figures