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تسجيل مستخدم جديدEventually, geometric $(n_{k})$ configurations exist for all $n$
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In a series of papers and in his 2009 book on configurations Branko Grunbaum described a sequence of operations to produce new $(n_{4})$ 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 $(n_{k})$ 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 $k$.
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