相关论文: Computing positroid cells in the Grassmannian of l…
Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. We prove his conjecture that a positroid is exactly an intersection of…
Postnikov constructed a decomposition of a totally nonnegative Grassmannian into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point belongs to and to determine affine coordinates of the…
Positroids are a family of matroids introduced by Postnikov in the study of non-negative Grassmannians. Postnikov identified several combinatorial objects in bijections with positroids, among which are bounded affine permutations. On the…
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…
A positroid is the matroid of a real matrix with nonnegative maximal minors, a positroid variety is the closure of the locus of points in a complex Grassmannian whose matroid is a fixed positroid, and a positroid class is the cohomology…
A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. Postnikov demonstrated that positroids are in bijection with certain interesting classes of…
Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics. The positroids give rise to determinantal equations…
Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics. The positroids give rise to determinantal equations…
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…
Bicolored tilings are given by a collection of smooth curves in a disk with a coloring map on the tiles these curves form. Postnikov diagrams can be viewed as the image of certain bicolored tilings under the Scott map. We introduce a…
A positroid is the matroid of a matrix whose maximal minors are all nonnegative. Given a permutation $w$ in $S_n$, the matroid of a generic $n \times n$ matrix whose non-zero entries in row $i$ lie in columns $w(i)$ through $n+i$ is an…
A positroid is an ordered matroid realizable by a real matrix with all nonnegative maximal minors. Postnikov gave a map from ordered matroids to Grassmann necklaces, for which there is a unique positroid in each fiber of the map. Here, we…
We initiate the study of a class of polytopes, which we coin polypositroids, defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes. Whereas positroids are the matroids arising…
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…
We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground…
A positroid is a special case of a realizable matroid that arose from the study of the totally nonnegative part of the Grassmannian by Postnikov. In this paper, we study the facets of its matroid polytope and the independent set polytope.…
Positroids are matroids realizable by real matrices with all nonnegative maximal minors. They partition the ordered matroids into equivalence classes, called positroid envelope classes, by their Grassmann necklaces. We give an explicit…
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…
The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial…
We study the boundaries of the positroid cells which arise from N = 4 super Yang Mills theory. Our main tool is a new diagrammatic object which generalizes the Wilson loop diagrams used to represent interactions in the theory. We prove…