Related papers: The free group in R
We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.
Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. It turns out that Stallings'…
We discuss a partial normalisation of a finite graph of finite groups $(\Gamma(-), X)$ which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result, this provides a flexible and rather useful tool in the…
Let $G$ be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of $G$ and a bound on the Pr\"{u}fer rank of $G$. This yields in turn an algorithm to decide whether a finitely…
We give two examples of a finitely generated subgroup of a free group and a subset, closed in the profinite topology of a free group, such that their product is not closed in the profinite topology of a free group.
This paper is the first in a sequence on the first order theory of free products. In the first paper we generalize the analysis of systems of equations over free and (torsion-free) hyperbolic groups, and analyze system of equations over…
We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with…
We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, P\'olya…
We present an effective algorithm for detecting automorphic orbits in free groups, as well as a number of algorithmic improvements of train tracks for free group automorphisms.
Let $F$ be a finitely generated free group. We present an algorithm such that, given a subgroup $H\leqslant F$, decides whether $H$ is the fixed subgroup of some family of automorphisms, or family of endomorphisms of $F$ and, in the…
CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows the user to formulate convex optimization problems in a natural mathematical syntax…
We introduce the free inhomogeneous wreath product of compact matrix quantum groups, which generalizes the free wreath product (Bichon 2004). We use this to present a general technique to determine quantum automorphism groups of connected…
Conducting research often involves managing multiple disconnected tools for survey design, data collection, response analysis, and report generation, leading to inefficiencies, increased error risks, and challenges in ensuring…
This article presents a machinery based on polyhedral products that produces faithful representations of graph products of finite groups and direct products of finite groups into automorphisms of free groups $\rm Aut(F_n)$ and outer…
We present Glyph - a Python package for genetic programming based symbolic regression. Glyph is designed for usage let by numerical simulations let by real world experiments. For experimentalists, glyph-remote provides a separation of…
The xdvir package provides functions for rendering LaTeX fragments as labels, annotations, and data symbols in R plots. There are convenient high-level functions for rendering LaTeX fragments, including labels on ggplot2 plots, plus…
We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.
In this article, we present a new R package fc that provides a streamlined, standard evaluation-based approach to function composition. Using fc, a sequence of functions can be composed together such that returned objects from composed…
We construct the free products of arbitrary digroups, and thus we solve an open problem of Zhuchok.
This paper presents an open-source, lightweight, yet comprehensive software framework, named RPC, which integrates physics-based simulators, planning and control libraries, debugging tools, and a user-friendly operator interface. RPC…