Related papers: The apparent structure of dense Sidon sets

Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

We extend fundamental results concerning Apollonian packings, which constitute a major object of study in number theory, to certain homogeneous sets that arise naturally in complex dynamics and geometric group theory. In particular, we give…

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

We study a certain class of simple abelian varieties of type $\mathrm{IV}$ (in Albert's classification) over number fields with Mumford-Tate groups of type $A$. In particular, we show that such abelian varieties have ordinary reduction away…

We introduce Cayley posets as posets arising naturally from pairs $S<T$ of semigroups, much in the same way that Cayley graph arises from a (semi)group and a subset. We show that Cayley posets are a common generalization of several known…

We consider certain Dirichlet series of Selberg type, constructed from periods of automorphic forms. We study analytic properties of these Dirichlet series and show that they have analytic continuation to the whole complex plane.

There are many examples for point sets in finite geometry, which behave "almost regularly" in some (well-defined) sense, for instance they have "almost regular" line-intersection numbers. In this paper we investigate point sets of a…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated…

Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson and Wei) we describe precise necessary and sufficient conditions for…

A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally…

We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely…

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case in which such graphs are Cayley graphs of Abelian groups. These groups can be constructed by…

We prove that maximal cardinality of the Sidon set from $[n]$ exceeds $\sqrt{n}

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression, or, more generally, with partitions into distinct parts of…

The nature and origin of exceptional sets associated with the rotation number of circle maps, Kolmogorov-Arnol'd-Moser theory on the existence of invariant tori and the linearisation of complex diffeomorphisms are explained. The metrical…

We study a family of graphs with diameter two and asymptotically optimal order for their maximum degree, obtained from perfect difference sets. We show that for all known examples of perfect difference sets, the graph we obtain is…

While the number of asteroids with known shapes has drastically increased over the past few years, little is known on the the time-evolution of shapes and the underlying physical processes. Here we propose an averaged abrasion model based…