9 citations · 16 across the 9 of their papers we have counts for
13 papers
Cayley graph diameters for fixed cycle types are eventually quasipolynomial
Andrei Smolensky
Given a cycle type, the corresponding conjugacy class of generates either or for sufficiently large . We prove that the sequence of diameters of Cayley graphs…
CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)
A. Chervov, D. Fedoriaka, E. Konstantinova +46
This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Pytho…
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces
Iskander Azangulov, Andrei Smolensky, Alexander Terenin +1
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used…
On power sum kernels on symmetric groups
Iskander Azangulov, Viacheslav Borovitskiy, Andrei Smolensky
In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups . Such processes are bi-invariant: the action…
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case
Iskander Azangulov, Andrei Smolensky, Alexander Terenin +1
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used…
Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels
Noémie Jaquier, Viacheslav Borovitskiy, Andrei Smolensky +3
Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these pr…
The centralizers of root subgroups in Kac-Moody Steinberg groups
Andrei Smolensky
For the affine and hyperbolic root system the symmetric part of the centralizers of root subgroups in the corresponding Steinberg groups are calculated. In the affine case the corr…
Real roots in the root system
Karin Baur, Jian-Rong Li, Andrei Smolensky
Motivated by the recent advances in the categorification of the cluster structure on the coordinate rings of Grassmannians of -subspaces in -space, we investigate a particula…
Suzuki-Ree groups and Tits mixed groups over rings
Andrei Smolensky
It is shown that Suzuki-Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This elimina…
On the definition of Suzuki groups over rings
Andrei Smolensky
The definition of Suzuki groups over rings is given by means of an explicit description as a difference-algebraic group. For a (not necessarily perfect) field with more than two el…
Decompositions of congruence subgroups of Chevalley groups
Sergey Sinchuk, Andrei Smolensky
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estim…
Products of Sylow subgroups in Suzuki and Ree groups
Andrei Smolensky
An explicit and elementary proof is given to the fact that Suzuki and Ree groups can be decomposed into the product of 4 of their Sylow p-subgroups, where p is the defining charact…
Commutator width of Chevalley groups over rings of stable rank 1
Andrei Smolensky
An estimate on the commutator width is given for Chevalley groups over rings of stable rank 1, and the general method suitable for other rings of small dimension.