Related papers: Central sets and infinite monochromatic exponentia…

Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…

Color centers are versatile systems that generate quantum light, sense magnetic fields and produce spin-photon entanglement. We review how these properties have pushed the limits of fundamental knowledge in a variety of scientific…

We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very…

In breakthrough results, Saxton-Thomason and Balogh-Morris-Samotij developed powerful theories of hypergraph containers. In this paper, we explore some consequences of these theories. We use a simple container theorem of Saxton-Thomason and…

An exactly solvable model is used to investigate the assumptions behind color transparency.

We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…

We provide a short proof of a conic version of the colorful Carath\'eodory theorem for oriented matroids. Holmsen's extension of the colorful Carath\'eodory theorem to oriented matroids (Advances in Mathematics, 2016) already encompasses…

Gy\'arf\'as famously showed that in every $r$-coloring of the edges of the complete graph $K_n$, there is a monochromatic connected component with at least $\frac{n}{r-1}$ vertices. A recent line of study by Conlon, Tyomkyn, and the second…

Erd\H{o}s and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and R\"odl asked whether there…

Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this…

Using Ravenel's Thom spectrum $X(n)$, we introduce the concept of chromatic defect, which measures how far a spectrum is from being complex-orientable. We compute the chromatic defect of various examples of interest, such as finite spectra,…

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…

Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…

We develop novel techniques which allow us to prove a diverse range of results relating to subset sums and complete sequences of positive integers, including solutions to several longstanding open problems. These include: solutions to the…

We prove a general large sieve statement in the context of random walks on subgraphs of a given graph. This can be seen as a generalization of previously known results where one performs a random walk on a group enjoying a strong spectral…

We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…

We study the list-chromatic number and the coloring number of graphs, especially uncountable graphs. We show that the coloring number of a graph coincides with its list-chromatic number provided that the diamond principle holds. Under the…

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…

The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…

Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and that form an arithmetic progression.…