Related papers: Product set phenomena for countable groups

We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the "productset property"). We first show that the productset property holds for any definable…

The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…

We present new, exceptionally efficient proofs of Poisson--Dirichlet limit theorems for the scaled sizes of irreducible components of random elements in the classic combinatorial contexts of arbitrary assemblies, multisets, and selections,…

Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…

In 2015, Phulara established a generalization of the famous central set theorem by an original idea. Roughly speaking, this idea extends a combinatorial result from one large subset of the given semigroup to countably many. In this paper,…

Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

We determine which of the finite-type Artin groups are locally indicable, and compute presentations for their commutator subgroups.

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…

The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…

Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

Let $\mathbf{G}$ be either a simple linear algebraic group over an algebraically closed field of positive characteristic or a quantum group at a root of unity. We define new classes of indecomposable $\mathbf{G}$-modules, which we call…

We give a general method to build categories of combinatorial manifolds, i.e. categories of combinatorial objects satisfying some local property at every "point", as coreflective subcategories of categories of relational presheaves. To do…

The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…