Related papers: On stretching the interval simplex-permutohedron

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the…

Given an $n$-gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace in this setting the $n$-gon (viewed as a disc with $n$…

A graph associahedron is a simple polytope whose face lattice encodes the nested structure of the connected subgraphs of a given graph. In this paper, we study certain graph properties of the 1-skeleta of graph associahedra, such as their…

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress…

Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an…

We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be…

Wythoff's construction associates a uniform polytope to a Coxeter diagram whose vertices are decorated with crosses, which indicate the subgroup stabilizing a generic point. Champagne, Kjiri, Patera, and Sharp remarked that by associating…

This paper introduces the geometric foundations for the study of the $s$-permutahedron and the $s$-associahedron, two objects that encode the underlying geometric structure of the $s$-weak order and the $s$-Tamari lattice. We introduce the…

The circuit diameter of a polyhedron is the maximum length (number of steps) of a shortest circuit walk between any two vertices of the polyhedron. Introduced by Borgwardt, Finhold and Hemmecke (SIDMA 2015), it is a relaxation of the…

Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many…

Given a shifted order ideal $U$, we associate to it a family of simplicial complexes $(\Delta_t(U))_{t\geq 0}$ that we call squeezed complexes. In a special case, our construction gives squeezed balls that were defined and used by Kalai to…

This is an English translation of the paper in which N. I. Akhiezer discovered his famous orthogonal polynomials on two intervals in a connection with a generalization of the Korkin-Zolotarev (Korkine-Zolotaref) problem (see the small…

We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n] that was first considered by Petersen, Pylyavskyy, Speyer (2010). We give an alternative approach to their result that the…

For any finite set $\A$ of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set $\A$, where a marked graph is defined as a…

We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…

There exist natural generalizations of the real moduli space of Riemann spheres based on manipulations of Coxeter complexes. These novel spaces inherit a tiling by the graph-associahedra convex polytopes. We obtain explicit configuration…

Fix a stable degree-$n$ rank-$k$ bundle $\mathcal{F}$ on a complex elliptic curve for (coprime) $1\le k<n\ge 3$. We identify the symplectic leaves of the Poisson structure introduced independently by Polishchuk and Feigin-Odesskii on…

Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \emph{generalized associahedron}. They provided an explicit realization of this…

Stanley's formula for the number of reduced expressions of a permutation regarded as a Coxeter group element raises the question of how to enumerate the reduced expressions of an arbitrary Coxeter group element. We provide a framework for…

We study the derived category of pseudo-coherent complexes over a noetherian commutative ring, building on prior work by Matsui-Takahashi. Our main theorem is a computation of the Balmer spectrum of this category in the case of a discrete…