On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups

no code implementations • 29 Jan 2021 • Oleg Karpenkov

In this paper we introduce two new algorithms in the spirit of Jacobi-Perron algorithm: the heuristic algebraic periodicity detecting algorithm and the $\sin^2$-algorithm.

Number Theory 11R16, 11H46, 11A05

On a periodic Jacobi-Perron type algorithm

no code implementations • 29 Jan 2021 • Oleg Karpenkov

In this paper we introduce a new modification of the Jacobi-Perron algorithm in three dimensional case and prove its periodicity for the case of totally-real conjugate cubic vectors.

Number Theory 11R16, 11H99, 11A05

Geometric criteria for realizability of tensegrities in higher dimensions

no code implementations • 5 Jul 2019 • Oleg Karpenkov, Christian Müller

In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities.

Combinatorics Metric Geometry 05C10, 52C25