3 papers
math.CO2020
On the Parallel Tower of Hanoi Puzzle: Acyclicity and a Conditional Triangle Inequality
Andrey Rukhin
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 th…
math.NT2018
A Dual-Radix Approach to Steiner's 1-Cycle Theorem
Andrey Rukhin
This article presents a variety of algebraic proofs of Steiner's -Cycle Theorem. It also demonstrates that, under an exponential upper-bound on the iterates, the only -cycles…
math.NT2015
A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits within Syracuse Dynamical Systems
Andrey Rukhin
This article analyzes the periodic orbits of Syracuse dynamical systems in a novel algebraic setting: the commutative ring of graded -adic integers. Within this context, this ar…