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- W2962768111 abstract "We study a non-trivial extreme case of the orchard problem for $12$ pseudolines and we provide a complete classification of pseudoline arrangements having $19$ triple points and $9$ double points. We have also classified those that can be realized with straight lines. They include new examples different from the known example of Boroczky. Since Melchior's inequality also holds for arrangements of pseudolines, we are able to deduce that some combinatorial point-line configurations cannot be realized using pseudolines. In particular, this gives a negative answer to one of Grunbaum's problems. We formulate some open problems which involve our new examples of line arrangements." @default.
- W2962768111 created "2019-07-30" @default.
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- W2962768111 date "2017-10-06" @default.
- W2962768111 modified "2023-10-03" @default.
- W2962768111 title "On the Sylvester–Gallai and the orchard problem for pseudoline arrangements" @default.
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- W2962768111 doi "https://doi.org/10.1007/s10998-017-0224-x" @default.
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