Related papers: Product set phenomena for countable groups
We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets. We link this with the inner measure of…
In [On $IP^{\star}$sets and central sets, Combinatorica, 14 (1994) 269-277], N. Hindman and V.Bergelson proved additive $IP^{\star}$-sets contain finite sums and finite products of a single sequence. An analogous study was made by A. Sisto…
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural…
We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups. While the decomposition is well understood for free…
We introduce a new probabilistic technique for finding 'almost-periods' of convolutions of subsets of groups. This gives results similar to the Bogolyubov-type estimates established by Fourier analysis on abelian groups but without the need…
When multitudes of features can plausibly be associated with a response, both privacy considerations and model parsimony suggest grouping them to increase the predictive power of a regression model. Specifically, the identification of…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
In the first part we construct some Buck measurable sets. In the second part we apply the Niven theorem for Buck's measure density to certain sets.
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on VC_ind-density, and…
In this paper we generalize a methodology [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Phys.: Condens. Matter {\bf 22}, 104102 (2010)] for dealing with the inference of bulk properties from small simulations of self-assembling…
We produce a large class of generalized cluster structures on the Drinfeld double of $\text{GL}_n$ that are compatible with Poisson brackets given by Belavin-Drinfeld classification. The resulting construction is compatible with the…
The study of symmetric structures is a new trend in Ramsey theory. Recently in [7], Di Nasso initiated a systematic study of symmetrization of classical Ramsey theoretical results, and proved a symmetric version of several Ramsey theoretic…
As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…
We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily sigma-additive. Using this, together with infinite-combinatorial methods and simple forcing theoretic methods,…