PARTITION-EQUIVALENT n-POINTS CONFIGURATIONS WITH TWO DISTANCES

Ali Asghar Rezaei

DOI Number
https://doi.org/10.22190/FUMI1904671R
First page
671
Last page
678

Abstract


In this paper we define an equivalence relation on the set of all possible geometrical models of M(n, k) containing n points in 3D Euclidean space having k distinct distances. We investigate the number of geometrical model for M(4,2), M(5,2) and M(6,2) up to the mentioned equivalence relation.

Keywords

Constructible models; distinct distances; partition-equivalent; geometrical model.

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References


L. Blumenthal: Theory and Applications of Distance Geometry. Oxford University Press, Oxford, 1953.

H. T. Croft: 9-point and 7-point configurations in 3-space. Proc. London Math. Soc. 12 (1962), 400–424.

G. Elekes and M. Sharir: Incidences in three dimensions and distinct distances in the plane. Combin. Probab. Comput. 20 (2011), 571–608.

L. Guth and N. H. Katz: On the Erds distinct distances problem in the plane. Ann. of Math. (2015), 155–190.

A. A. Rezaei: On the geometric structures with n points and k distances. Electron. Notes Discrete Math. 45 (2014), 181–186.

A. A. Rezaei: On the Configurations with n Points and Two Distances. Math. Int. Res. DOI: 10.22052/mir.2017.81496.1056

G. Tardos: On distinct sums and distinct distances. Adv. Math. 180 (2003), 275–289.




DOI: https://doi.org/10.22190/FUMI1904671R

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