• 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}
}

• L. Berman, G'abor G'evay, +7 authors U. Ljubljana
• Published 31 March 2021
• Mathematics

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 results for k = 2, 3, 4, and some more detailed analysis to improve the upper bound for larger values of k.