Related papers: Experiments on growth series of braid groups

We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although…

The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These…

We present two quite different algorithms to compute the number of elements in the sphere of radius $n$ of Thompson's group $F$ with standard generating set. The first of these requires exponential time and polynomial space, but…

Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…

Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we…

We attach to every Coxeter system (W,S) an extension C_W of the corresponding Iwahori-Hecke algebra. We construct a 1-parameter family of (generically surjective) morphisms from the group algebra of the corresponding Artin group onto C_W.…

We give a computational algorithm which decides if a braid is quasipositive or not. A braid is quasipositive if it's a product of conjuguates of generators. For this, we use the theory of Garside and the combinatorials properties of the…

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series…

Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic…

We study a family of lattice-gas systems defined on semiregular grids, obtained by projecting the vertices of three different geodesic icosahedra onto a spherical surface. By using couplings up to third neighbors we explore various…

We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The fusion rules induce an association scheme with Krein…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

Let f be a nondegenerate quadratic form in at least 5 variables over a number field K and let S be a finite set of valuations of K containing all Archimedean ones. We prove that if the Witt index of f is at least 2 or it is 1 and S contains…

In this paper, we study geodesic growth of numbered graph products; these are a generalization of right-angled Coxeter groups, defined as graph products of finite cyclic groups. We first define a graph-theoretic condition called…

Let $\beta:=\sigma_1\sigma_2^{-1}$ be a braid in $B_3$, where $B_3$ is the braid group on 3 strings and $\sigma_1, \sigma_2$ are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number $n$ not…

The orbifold braid groups of two dimensional orbifolds were defined in [1] (arXiv:math/9907194) to understand certain Artin groups as subgroups of some suitable orbifold braid groups. We studied orbifold braid groups in some more detail in…

Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a…

We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy…

We compute the structure of the Lie algebras associated to two examples of branch groups, and show that one has finite width while the other, the ``Gupta-Sidki group'', has unbounded width. This answers a question by Sidki. More precisely,…