arXiv subjects

Andrey Rukhin

Publications and source records attributed to Andrey Rukhin.

3 recordsLinked to original sources

arXiv2022

On the Parallel Tower of Hanoi Puzzle: Acyclicity and a Conditional Triangle Inequality

A parallel variant of the Tower of Hanoi Puzzle is described herein. Within this parallel context, two theorems on minimal walks in the state space of configurations, along with their constructive proofs, are provided. These proofs are used to describe a {\sl denoising method}: a method for identifying and eliminating sub-optimal transfers within an arbitrary, valid sequence of disk configurations (as per the rules of the Puzzle). We discuss potential applications of this method to hierarchical reinforcement learning.

math.CO↗

arXiv2019

A Dual-Radix Approach to Steiner's 1-Cycle Theorem

This article presents a variety of algebraic proofs of Steiner's $1$-Cycle Theorem. It also demonstrates that, under an exponential upper-bound on the iterates, the only $1$-cycles in the (accelerated) $3x-1$ dynamical system are $(1)$ and $(5,7)$.

math.NT↗

arXiv2018

A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits within Syracuse Dynamical Systems

This article analyzes the periodic orbits of Syracuse dynamical systems in a novel algebraic setting: the commutative ring of graded $n$-adic integers. Within this context, this article introduces a dual-radix modular division algorithm for computing the graded canonical expansions and graded quotients for a certain class of rational expressions that arise from periodic orbits within these dynamical systems. This division algorithm yields two novel methods for testing the integrality of the Böhm-Sontacchi numbers.

math.NT↗