Related papers: Constructive Membership Tests in Some Infinite Mat…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This is based on a new proof of the result (in more general form…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
For any conjugacy class C in G=PSL(2,q) we compute C^2 and discuss whether C contains a triple of elements whose product is 1 which generate G. Moreover, we determine which elements in G can be written as a product of two conjugate elements…
Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their…
We answer a question raised by Lanier about the possibility of generating $A_n$ and $S_n$ with two elements of order $k$, where $n \geqslant k \geqslant 3$. We show that this can always be done apart from some clear exceptions.
We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…
Natural Language Generation systems typically have two parts - strategic ('what to say') and tactical ('how to say'). We present our experiments in building an unsupervised corpus-driven template based tactical NLG system. We consider…
Fix a finite set $S \subset {GL}(k,\mathbb{Z})$. Denote by $a_n$ the number of products of matrices in $S$ of length $n$ that are equal to 1. We show that the sequence $\{a_n\}$ is not always P-recursive. This answers a question of…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…
This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the…
Let $S(n)$ be the infinite-type surface with infinite genus and $n \in \mathbb{N}$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\mod(S(n))$, is a Polish group that is not countably generated, but it…
A new set of elementary symplectic elements is described, It is shown that these also generate the elementary symplectic group {\rm ESp}$_{2n}(R)$. These generators are more symmetrical than the usual ones, and are useful to study the…
We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence…
Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they…
Expressive range analysis is a visualization-based technique used to evaluate the performance of generative models, particularly in game level generation. It typically employs two quantifiable metrics to position generated artifacts on a 2D…