P-associahedra

• Pavel Galashin ^[1]
  1. [1] University of California System

     University of California System

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, págs. 1-34
• Idioma: inglés
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• Resumen

  • 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 → 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