Related papers: Non-Additive Discrepancy: Coverage Functions in a …
It is proved that 1) the indicator function of some onefold or multifold independent set in a regular graph is a perfect coloring if and only if the set attain the Delsarte--Hoffman bound; 2) each transversal in a uniform regular hypergraph…
Assuming the abundance conjecture in dimension $d$, we establish a non-algebraicity criterion of foliations: any log canonical foliation of rank $\le d$ with $\nu\neq\kappa$ is not algebraically integrable, answering question of…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…
The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to…
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley--Stembridge…
We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…
As the most powerful tool in discrepancy theory, the partial coloring method has wide applications in many problems including the Beck-Fiala problem and Spencer's celebrated result. Currently, there are two major algorithmic methods for the…
Non-Archimedean mathematics (in particular, nonstandard analysis) allows to construct some useful models to study certain phenomena arising in PDE's; for example, it allows to construct generalized solutions of differential equations and…
DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvo\v{r}\'{a}k and Postle in 2015. The chromatic polynomial of a graph is an…
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at any time, any sequence of p(k) consecutive points, for some…
In 1981, Beck and Fiala [Discrete Appl. Math, 1981] conjectured that given a set system $A \in \{0,1\}^{m \times n}$ with degree at most $k$ (i.e., each column of $A$ has at most $k$ non-zeros), its combinatorial discrepancy…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of…
Motivated by the study of Macdonald polynomials, J. Haglund and A. Wilson introduced a nonsymmetric polynomial analogue of the chromatic quasisymmetric function called the \emph{chromatic nonsymmetric polynomial} of a Dyck graph. We give a…
Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are $n$ elements and $m$ sets and each element lies in $t$ randomly chosen sets. In this setting, Ezra and Lovett showed an $O((t \log t)^{1/2})$…
A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(n^1/2). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In…
We prove a Hopf-type lemma for antisymmetric super-solutions to the Dirichlet problem for the fractional Laplacian with zero-th order terms. As an application, we use such a Hopf-type lemma in combination with the method of moving planes to…