# Connected geometric (n_k) configurations exist for almost all n

@article{Gvay2021ConnectedG, title={Connected geometric (n\_k) configurations exist for almost all n}, author={G{\'a}bor E. G{\'e}vay and Leah Wrenn Berman and Toma{\vz} Pisanski}, journal={The Art of Discrete and Applied Mathematics}, year={2021} }

In a series of papers and in his 2009 book on configurations Branko Grunbaum described a sequence of operations to produce new (n4) configurations from various input configurations. These operations were later called the “Grunbaum 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…

## One Citation

New bounds on the existence of $(n_{5})$ and $(n_{6})$ configurations: the Gr\"{u}nbaum Calculus revisited

- Mathematics
- 2022

. The “Gr¨unbaum Incidence Calculus” is the common name of a collection of operations introduced by Branko Gr¨unbaum to produce new ( n 4 ) conﬁgurations from various input conﬁgurations. In a…

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