Related papers: Model Theory of Homogeneous D-sets
The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…
In this paper, we consider dominating sets $D$ and $D'$ such that $D$ and $D'$ are disjoint and there exists a perfect matching between them. Let $DD_{\textrm{m}}(G)$ denote the cardinality of smallest such sets $D, D'$ in $G$ (provided…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…
For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k…
We describe families of plane-filling curves on any edge-to-edge tiling of the plane with regular polygons and finitely many classes of edges. It is shown how to partition the minimal number of edge classes from the group G of symmetries of…
An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are…
Z. Wen and J. Wu introduced the notion of homogeneous perfect sets as a generalization of Cantor type sets and determined their exact Hausdorff dimension based on the length of their fundamental intervals and the gaps between them. In this…
We study Koebe orderings of planar graphs: vertex orderings obtained by modelling the graph as the intersection graph of pairwise internally-disjoint discs in the plane, and ordering the vertices by non-increasing radii of the associated…
We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A series given by Brubaker, Bump, Friedberg,…
We observe that the nonstandard finite cardinality of a definable set in a strongly minimal pseudofinite structure D is a polynomial over the integers in the nonstandard finite cardinality of D. We conclude that D is unimodular, hence also…
An edge-coloring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Lehner, Pil\'{s}niak, and Stawiski proved that all connected regular graphs except $K_2$ admit an asymmetric edge-coloring with…
We classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by F. Kwakkel, T.J\"ager and A. Passeggi in the torus. The…
In this contribution we summarize our recent progress in understanding the relation between ${\cal N} = 1$ superconformal indices and relativistic elliptic integrable models. We start briefly reviewing the emergence of such models in…
We show that the model of discrete spaces that we have proposed in previous contributions gives a comprehensive and detailed interpretation of the properties of the standard model of particles. Moreover the model also suggests the possible…
We demonstrate the existence of a uniform and nonhomogeneous vector bundle $E$ of rank $(n-d)(m+1)-1$ over Grassmannian $\mathbb{G}(d,n)$, where $m>d$ and $1\le d \le n-d-1$ with a $\mathbb{P}$-homogeneity degree $h(E)=d$. Particularly, we…
R.M. Green described structural properties that ``doubly infinite'' colored posets should possess so that they can be used to construct representations of most affine Kac--Moody algebras. These representations are analogs of the minuscule…
In this paper, we introduce the category of quasi-tempered automorphic D-modules, which is a rather natural class of D-modules from the point of view of geometric Langlands. We provide a characterization of this category in terms of…