Related papers: Stratifications on the Ran space
We prove the existence of a model structure on the category of stratified simplicial sets whose fibrant objects are precisely $n$-complicial sets, which are a proposed model for $(\infty,n)$-categories, based on previous work of Verity and…
We study the class of discrete measures in the complex plain with the following property: up to a finite number, all zeros of any Cauchy transform of the measure (with $\ell^2$-data) are localized near the support of the measure. We find…
We introduce a new notion of stratification (``riso-stratification''), which is canonical and which exists in a variety of settings, including different topological fields like $\mathbb{C}$, $\mathbb{R}$ and $\mathbb{Q}_p$, and also…
We construct and study the space C(\R^d,n) of all partitions of \R^d into n non-empty open convex regions (n-partitions). A representation on the upper hemisphere of an n-sphere is used to obtain a metric and thus a topology on this space.…
We give formulas for enumerating directed paths in the graded poset of semi-magic squares of size three. We give two applications of these formulas: an advanced example of Vandermonde convolution for finite graded posets, and a direct…
We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…
We obtain some $L^2$ results for the Cauchy-Riemann operator on forms that vanish to high order near the singular set of a complex space.
In this paper we discuss several results about the structure of the configuration space of two-dimensional tensegrities with a small number of points. We briefly describe the technique of surgeries that is used to find geometric conditions…
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…
In this note we introduce a new approach to rough and stochastic partial differential equations (RPDEs and SPDEs): we consider general Banach spaces as state spaces and -- for the sake of simiplicity -- finite dimensional sources of noise,…
Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric monoidal category, where the monoidal product is the direct sum…
In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the…
We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm computes a stratification $\pi$ of the poset $P$ of…
The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In…
The sequence space of all real-valued sequences, denoted $Seq(\mathbb{R})$, is typically investigated through the lens of infinite-dimensional vector spaces, utilizing Banach space norms or Schauder bases. This work proposes a…
In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…
A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…
Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlaying structure of "supertropical trigonometry" and thereby a version of convex geometry which is compatible with quasilinearity.…