Eventually, geometric $(n_{k})$ configurations exist for all $n$
Combinatorics
2021-04-02 v1
Abstract
In a series of papers and in his 2009 book on configurations Branko Gr\"unbaum described a sequence of operations to produce new configurations from various input configurations. These operations were later called the "Gr\"unbaum Incidence Calculus". We generalize two of these operations to produce operations on arbitrary configurations. Using them, we show that for any there exists an integer such that for any there exists a geometric configuration. We use empirical results for , and some more detailed analysis to improve the upper bound for larger values of .
Cite
@article{arxiv.2104.00045,
title = {Eventually, geometric $(n_{k})$ configurations exist for all $n$},
author = {Leah Wrenn Berman and Gábor Gévay and Tomaž Pisanski},
journal= {arXiv preprint arXiv:2104.00045},
year = {2021}
}