Related papers: Growth in groups: ideas and perspectives

Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…

This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a…

It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is combinatorial and notoriously…

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and…

Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric…

This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional…

Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…

This paper surveys some results and methods in topological transformation groups.

This is a survey of results on partially commutative groups and partially commutative algebras.

Let G be a semisimple Lie group with associated symmetric space D, and let Gamma subset G be a cocompact arithmetic group. Let L be a lattice inside a Z Gamma-module arising from a rational finite-dimensional complex representation of G.…

Let $\Gamma$ be a finite connected graph and $G$ a vertex-transitive group of its automorphisms. The pair $(\Gamma, G)$ is said to be locally-$L$ if the permutation group induced by the action of the vertex-stabiliser $G_v$ on the set of…

Given a set $I \subseteq \mathbb{N}$, consider the sequences $\{d_n(I)\},\{p_n(I)\}$ where for any $n$, $d_n(I)$ and $p_n(I)$ respectively count the number of permutations in the symmetric group $\mathfrak{S}_n$ whose descent set…

We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…

In this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we deduce that the associated relative growth series fail to be…

Picking permutations at random, the expected number of k-cycles is known to be 1/k and is, in particular, independent of the size of the permuted set. This short note gives similar size-independent statistics of finite general linear…

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…

We develop further Cannon's method of cone types for finding the growth function of a group, which can also be used to find the coordination sequences of certain infinite graphs. We then apply this method to compute the growth functions and…

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

Let $G$ be an acylindrically hyperbolic group on a $\delta$-hyperbolic space $X$. Assume there exists $M$ such that for any finite generating set $S$ of $G$, the set $S^M$ contains a hyperbolic element on $X$. Suppose that $G$ is…

Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…