Related papers: Neighborliness of Marginal Polytopes
The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan…
Quantum measurements often exhibit non-classical features, such as contextuality, which generalizes Bell's non-locality and serves as a resource in various quantum computation models. Existing frameworks have rigorously captured these…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or…
The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is…
We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum…
Algebras defined over fields of characteristic zero and positive characteristic usually do not behave the same way. However, for certain algebras, for example the group algebras, they behave the same way as the characteristic zero case at…
Moderately close binaries are a special class of targets for planet searches. From a theoretical standpoint, their hospitality to giant planets is uncertain and debated. From an observational standpoint, many of these systems present…
Let $f_i(P)$ denote the number of $i$-dimensional faces of a convex polytope $P$. Furthermore, let $S(n,d)$ and $C(n,d)$ denote, respectively, the stacked and the cyclic $d$-dimensional polytopes on $n$ vertices. Our main result is that for…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
To every partial order P, one associates a polynomial $\mathbb{D}_P$ in 4 variables that enumerates the intervals of P according to 4 parameters. Some symmetry properties of this polynomial are obtained for a specific family of posets, the…
For a diagram of simplicial combinatorial model categories, we show that the associated lax limit, endowed with the projective model structure, is a presentation of the lax limit of the underlying $\infty$-categories. Our approach can also…
In this paper, we introduce the n-th discrete topological complexity and study its properties such as its relation with simplicial Lusternik-Schnirelmann category and how the higher dimensions of discrete topological complexity relate with…
Many (if not most) of convex polytopes, important for combinatorial and algebraic geometry, are closely related to secondary polytopes of point configurations, or base polytopes of submodular functions, or their numerous variations and…
In this paper together with the preceding Part I \cite{CHR}, we develop a framework for tame geometry on Henselian valued fields of characteristic zero, called Hensel minimality. It adds to \cite{CHR} the treatment of the mixed…