LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop