$P$-associahedra
| Autor: | Galashin, Pavel |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 30 pages, 10 figures; v2: minor bibliography updates; v3: updated title and terminology. Final version to appear in Selecta Mathematica |
| Databáze: | arXiv |
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