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2020 Characterizing optimal point sets determining one distinct triangle
Hazel N. Brenner, James S. Depret-Guillaume, Eyvindur A. Palsson, Robert Stuckey
Involve 13(1): 91-98 (2020). DOI: 10.2140/involve.2020.13.91

Abstract

We determine the maximum number of points in d which form exactly t distinct triangles, where we restrict ourselves to the case of t = 1 . We denote this quantity by F d ( t ) . It is known from the work of Epstein et al. (Integers 18 (2018), art. id. A16) that F 2 ( 1 ) = 4 . Here we show somewhat surprisingly that F 3 ( 1 ) = 4 and F d ( 1 ) = d + 1 , whenever d 3 , and characterize the optimal point configurations. This is an extension of a variant of the distinct distance problem put forward by Erdős and Fishburn (Discrete Math. 160:1-3 (1996), 115–125).

Citation

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Hazel N. Brenner. James S. Depret-Guillaume. Eyvindur A. Palsson. Robert Stuckey. "Characterizing optimal point sets determining one distinct triangle." Involve 13 (1) 91 - 98, 2020. https://doi.org/10.2140/involve.2020.13.91

Information

Received: 12 February 2019; Revised: 29 September 2019; Accepted: 11 November 2019; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07172113
MathSciNet: MR4059943
Digital Object Identifier: 10.2140/involve.2020.13.91

Subjects:
Primary: 52C10
Secondary: 52C35

Rights: Copyright © 2020 Mathematical Sciences Publishers

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