[图书][B] Geometry of continued fractions
ON Karpenkov - 2022 - books.google.com
This book introduces a new geometric vision of continued fractions. It covers several
applications to questions related to such areas as Diophantine approximation, algebraic …
applications to questions related to such areas as Diophantine approximation, algebraic …
Boundary patrolling by mobile agents with distinct maximal speeds
A set of k mobile agents are placed on the boundary of a simply connected planar object
represented by a cycle of unit length. Each agent has its own predefined maximal speed …
represented by a cycle of unit length. Each agent has its own predefined maximal speed …
Some remarks on the lonely runner conjecture
T Tao - arXiv preprint arXiv:1701.02048, 2017 - arxiv.org
The lonely runner conjecture of Wills and Cusick, in its most popular formulation, asserts that
if $ n $ runners with distinct constant speeds run around a unit circle ${\bf R}/{\bf Z} $ starting …
if $ n $ runners with distinct constant speeds run around a unit circle ${\bf R}/{\bf Z} $ starting …
Linear search by a pair of distinct-speed robots
Two mobile robots are initially placed at the same point on an infinite line. Each robot may
move on the line in either direction not exceeding its maximal speed. The robots need to find …
move on the line in either direction not exceeding its maximal speed. The robots need to find …
From rainbow to the lonely runner: a survey on coloring parameters of distance graphs
DDF Liu - Taiwanese Journal of Mathematics, 2008 - projecteuclid.org
Motivated by the plane coloring problem, Eggleton, Erd\H {o} s and Skelton initiated the
study of distance graphs. Let $ D $ be a set of positive integers. The distance graph …
study of distance graphs. Let $ D $ be a set of positive integers. The distance graph …
[HTML][HTML] On the chromatic number of circulant graphs
J Barajas, O Serra - Discrete mathematics, 2009 - Elsevier
Given a set D of a cyclic group C, we study the chromatic number of the circulant graph G (C,
D) whose vertex set is C, and there is an edge ij whenever i− j∈ D∪− D. For a fixed set …
D) whose vertex set is C, and there is an edge ij whenever i− j∈ D∪− D. For a fixed set …
Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
Tao (2018) showed that in order to prove the Lonely Runner Conjecture (LRC) up to $ n+ 1$
runners it suffices to consider positive integer velocities in the order of $ n^{O (n^ 2)} …
runners it suffices to consider positive integer velocities in the order of $ n^{O (n^ 2)} …
On fence patrolling by mobile agents
Suppose that a fence needs to be protected (perpetually) by $ k $ mobile agents with
maximum speeds $ v_1,\ldots, v_k $ so that no point on the fence is left unattended for more …
maximum speeds $ v_1,\ldots, v_k $ so that no point on the fence is left unattended for more …
Deep lattice points in zonotopes, lonely runners, and lonely rabbits
M Beck, M Schymura - International Mathematics Research …, 2024 - academic.oup.com
Let be a polytope and let be an interior point of. The coefficient of asymmetry of about has
been studied extensively in the realm of Hensley's conjecture on the maximal volume of a …
been studied extensively in the realm of Hensley's conjecture on the maximal volume of a …
Correlation among runners and some results on the lonely runner conjecture
G Perarnau, O Serra - arXiv preprint arXiv:1407.3381, 2014 - arxiv.org
The Lonely Runner Conjecture was posed independently by Wills and Cusick and has many
applications in different mathematical fields, such as diophantine approximation. This well …
applications in different mathematical fields, such as diophantine approximation. This well …