Bounds on distinct and repeated dot product trees
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916394534174720 |
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| author | Autry, Aaron Gunter, Slade Housholder, Christopher Senger, Steven |
| author_facet | Autry, Aaron Gunter, Slade Housholder, Christopher Senger, Steven |
| contents | We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the plane that are described by weighted trees. We give new lower bounds on the number of distinct sets of dot products serving as weights for a given type of tree in any large finite point set. We also as demonstrate the existence of many repetitions of some special sets of dot products occurring in a given type of tree in different constructions, narrowing gap between the best known upper and lower bounds on these configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on distinct and repeated dot product trees Autry, Aaron Gunter, Slade Housholder, Christopher Senger, Steven Combinatorics 51A20, 52C10 We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the plane that are described by weighted trees. We give new lower bounds on the number of distinct sets of dot products serving as weights for a given type of tree in any large finite point set. We also as demonstrate the existence of many repetitions of some special sets of dot products occurring in a given type of tree in different constructions, narrowing gap between the best known upper and lower bounds on these configurations. |
| title | Bounds on distinct and repeated dot product trees |
| topic | Combinatorics 51A20, 52C10 |
| url | https://arxiv.org/abs/2409.09683 |