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Corpus ID: 232478536

Eventually, geometric $(n_{k})$ configurations exist for all $n$

@inproceedings{Berman2021EventuallyG,
title={Eventually, geometric \$(n\_\{k\})\$ configurations exist for all \$n\$},
author={Leah Wrenn Berman and G'abor G'evay and Tomavz Pisanski University of Alaska Fairbanks and Bolyai Institute and University of Szeged and University of Primorska and Institute of Applied Mathematics and Physics and Mechanics and University of Ljubljana},
year={2021}
}

In a series of papers and in his 2009 book on configurations Branko Grünbaum described a sequence of operations to produce new (n4) configurations from various input configurations. These operations were later called the “Grünbaum Incidence Calculus”. We generalize two of these operations to produce operations on arbitrary (nk) configurations. Using them, we show that for any k there exists an integer Nk such that for any n ≥ Nk there exists a geometric (nk) configuration. We use empirical… Expand

A geometric (nk) configuration is a collection of points and straight lines, typically in the Euclidean plane, so that each line passes through k of the points and each of the points lies on k of the… Expand

We present a technique to produce arrangements of lines with nice properties. As an application, we construct $(22_4)$ and $(26_4)$ configurations of lines. Thus concerning the existence of geometric… Expand

The motivation is the problem of the existence of $(n_4)$ configurations, still open for few remaining values of $n, which is based on quasi-configurations: point-line incidence structures where each point is incident to at least $3$ lines and each line is incidentto at least$3$ points.Expand

This paper is an introduction to Riemannian and semi-Riemannian manifolds of constant sectional curvature. We will introduce the concepts of moving frames, curvature, geodesics and homogeneity on six… Expand