Related papers: Polypositroids
Generalized permutahedra are a family of polytopes with a rich combinatorial structure and strong connections to optimization. We prove that they are the universal family of polyhedra with a certain Hopf algebraic structure. Their antipode…
Matroids give rise to several natural constructions of polytopes. Inspired by this, we examine polytopes that arise from the signed circuits of an oriented matroid. We give the dimensions of these polytopes arising from graphical oriented…
The symmetric edge polytope (SEP) of a (finite, undirected) graph is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. SEPs have been studied extensively in the past twenty years. Recently,…
Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Pl\"ucker coordinates vanish and which don't --- the set of nonvanishing Pl\"ucker coordinates forms a well-studied object called a…
The hypersimplex $\Delta_{k+1,n}$ is the image of the positive Grassmannian $Gr^{\geq 0}_{k+1,n}$ under the moment map. It is a polytope of dimension $n-1$ in $\mathbb{R}^n$. Meanwhile, the amplituhedron $\mathcal{A}_{n,k,2}(Z)$ is the…
We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial…
A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over $\mathbb{R}$, each $r$ by $r$ submatrix of which has nonnegative determinant. Earlier characterizations of connected positroids and…
This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…
We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence…
Nestohedra are a family of convex polytopes that includes permutohedra, associahedra, and graph associahedra. In this paper, we study an extension of such polytopes, called extended nestohedra. We show that these objects are indeed the…
The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-level matroids generalize series-parallel graphs, which have been already…
Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We…
A positroid is a matroid defined by Postnikov to study the cells in the non-negative part of the Grassmannian. They are in bijection with decorated permutations. We show a way to explain contraction and restriction of positroids in terms of…
We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type $B_d$. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension $d$ whose…
In this paper, we study positroids and its overlap with two classes of matroids: transversal and paving matroids. We exhibit a new class of fundamental transversal matroids and classify the Le-diagram for rank two transversal positroids. We…
A graph associahedron is a polytope dual to a simplicial complex whose elements are induced connected subgraphs called tubes. Graph associahedra generalize permutahedra, associahedra, and cyclohedra, and therefore are of great interest to…
Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and are known by previous work to be associated to positroids. We characterize the conditions under which two Wilson loop diagrams give the…
The stratification of the Grassmannian by positroid varieties has been the subject of extensive research. Positroid varieties are in bijection with a number of combinatorial objects, including $k$-Bruhat intervals and bounded affine…
A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of…
A magmoid is a non-empty set with a partial binary operation; group-like magmoids generalize group-like magmas such as semigroups, monoids and groups. In this article, we first consider the many ways in which the notions of associative…