# Poset associahedra

@inproceedings{Galashin2021PosetA, title={Poset associahedra}, author={Pavel Galashin}, year={2021} }

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 order-preserving maps P → R. Motivated by the study of totally nonnegative critical varieties in the Grassmannian, we introduce affine poset…

## One Citation

Critical varieties in the Grassmannian

- Mathematics, Physics
- 2021

We introduce a family of spaces called critical varieties. Each critical variety is a subset of one of the positroid varieties in the Grassmannian. The combinatorics of positroid varieties is…

## References

SHOWING 1-10 OF 52 REFERENCES

Coxeter Complexes and Graph-Associahedra

- Mathematics
- 2004

Abstract Given a graph Γ , we construct a simple, convex polytope, dubbed graph-associahedra , whose face poset is based on the connected subgraphs of Γ . This provides a natural generalization of…

Associahedron, cyclohedron and permutohedron as compactifications of configuration spaces

- Mathematics
- 2006

As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The…

Two poset polytopes

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 1986

A transfer map allows us to transfer properties of ϑ(P) to ℒ(P), and to transfer known inequalities involving linear extensions ofP to some new inequalities.

The Associahedron and Triangulations of the n-gon

- Computer Science, MathematicsEur. J. Comb.
- 1989

It is proved that Σn is isomorphic to the boundary complex of some (n − 3)-dimensional simplicial convexpolytope, and that this polytope can be geometrically realized to have the dihedral group Dn as its group of symmetries.

Convex polytopes from nested posets

- Mathematics, Computer ScienceEur. J. Comb.
- 2015

A new family of simple convex polytopes obtained by iterated truncations is led to, which generalize graph associahedra and nestohedra, even encompassing notions of nestings on CW-complexes.

A type-B associahedron

- Mathematics, Computer ScienceAdv. Appl. Math.
- 2003

This work proposes a B-analogue of the associahedron, a simplicial polytope whose h- vector is given by the rank-sizes of the type-B noncrossing partition lattice, just as the h-vector of the (simplicial type-A) assocIAhedron isgiven by the Narayana numbers.

Arithmetic of Marked Order Polytopes, Monotone Triangle Reciprocity, and Partial Colorings

- Computer Science, MathematicsSIAM J. Discret. Math.
- 2014

The marked order polytope parametrizes the order preserving extensions of F to P and the function counting integral-valued extensions is a piecewise polynomial in F and a reciprocity statement is proved in terms of order-reversing maps.

Alcoved Polytopes, I

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 2007

The aim of this paper is to study alcoved polytopes, which are poly topes arising from affine Coxeter arrangements, and to give a combinatorial formula for volumes of thesepolytopes.

The type $B$ permutohedron and the poset of intervals as a Tchebyshev transform

- Mathematics
- 2020

We show that the order complex of intervals of a poset, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the original poset. Besides studying the properties of this…

Matroid polytopes, nested sets and Bergman fans

- Mathematics
- 2004

The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present…