Related papers: Stratifications on the Ran space

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices…

We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.

We prove the existence of "half-plane differentials" with prescribed local data on any Riemann surface. These are meromorphic quadratic differentials with higher-order poles which have an associated singular flat metric isometric to a…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

We define a global rank for partial types based in a generalization of Shelah trees. We prove an equivalence with the depth of a localized version of the constructions known as dividing sequence and dividing chain. This rank characterizes…

In this paper, we explore the radial projection method for locally finite point sets and provide numerical examples for different types of order. The main question is whether the method is suitable to analyse order in a quantitive way. Our…

After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility…

The canonical map from the Kan subdivision of a product of finite simplicial sets to the product of the Kan subdivisions is a simple map, in the sense that its geometric realization has contractible point inverses.

We exhibit an identity of abstract simplicial complexes between the well-studied complex of trees and the reduced minimal nested set complex of the partition lattice. We conclude that the order complex of the partition lattice can be…

In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…

Schur-Szego composition of polynomials of degree N introduces an interesting semigroup structure on polynomial spaces. In this note we show how it interacts with the stratification of polynomials according to the multiplicity of their zeros…

By a theorem of A.Bj\"orner, for every interval $[u,v]$ in the Bruhat order of a Coxeter group $W$, there exists a stratified space whose strata are labeled by the elements of $[u,v]$, adjacency is described by the Bruhat order, and each…

The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a polynomial. In this paper, we consider…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic…

Let $G$ be a complete graph with $n+1$ vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with…

We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number…

Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…

Let $P\subset\mathbb R^n$ be a convex polytope and let $\ell$ be a linear functional which is nonconstant on every edge of $P$. The induced acyclic orientation determines positive and negative Bia{\l}ynicki-Birula type partitions of $P$…

The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the…