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- W4287249907 abstract "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 $k$." @default.
- W4287249907 created "2022-07-25" @default.
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- W4287249907 date "2021-03-31" @default.
- W4287249907 modified "2023-09-28" @default.
- W4287249907 title "Eventually, geometric $(n_{k})$ configurations exist for all $n$" @default.
- W4287249907 doi "https://doi.org/10.48550/arxiv.2104.00045" @default.
- W4287249907 hasPublicationYear "2021" @default.
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