Eventually, geometric $(n_{k})$ configurations exist for all $n$
Abstract
In a series of papers and in his 2009 book on configurations Branko Grünbaum described a sequence of operations to produce new $(n_{4})$ 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 $(n_{k})$ configurations. Using them, we show that for any $k$ there exists an integer $N_k$ such that for any $n \geq N_k$ there exists a geometric $(n_k)$ configuration. We use empirical results for $k = 2, 3, 4$, and some more detailed analysis to improve the upper bound for larger values of $k$.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2104.00045
 Bibcode:
 2021arXiv210400045W
 Keywords:

 Mathematics  Combinatorics;
 51A45;
 51A20;
 05B30;
 51E30