Sets in ℝd determining k taxicab distances
| Autor: | Lo Phillips, Vajresh Balaji, Solomon Mcharo, Bineyam Tsegaye, Anne Marie Loftin, Alex Rice, Olivia Edwards |
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| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
010102 general mathematics Dimension (graph theory) Discrete geometry Inverse 0102 computer and information sciences 01 natural sciences Combinatorics Euclidean distance 010201 computation theory & mathematics Metric (mathematics) Distance problem 0101 mathematics Geometric combinatorics Resolution (algebra) Mathematics |
| Zdroj: | Involve, a Journal of Mathematics. 13:487-509 |
| ISSN: | 1944-4184 1944-4176 |
| DOI: | 10.2140/involve.2020.13.487 |
| Popis: | We address an analog of a problem introduced by Erdős and Fishburn, itself an inverse formulation of the famous Erdős distance problem, in which the usual Euclidean distance is replaced with the metric induced by the l1-norm, commonly referred to as the taxicab metric. Specifically, we investigate the following question: given d,k∈ℕ, what is the maximum size of a subset of ℝd that determines at most k distinct taxicab distances, and can all such optimal arrangements be classified? We completely resolve the question in dimension d=2, as well as the k=1 case in dimension d=3, and we also provide a full resolution in the general case under an additional hypothesis. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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