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Plane point sets with many squares or isosceles right triangles

Title data

Kurz, Sascha:
Plane point sets with many squares or isosceles right triangles.
Bayreuth , 2021 . - 31 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005936

Official URL: Volltext

Abstract in another language

How many squares are spanned by n points in the plane? Here we study the corresponding maximum possible number of squares and determine the exact values for all n≤17. For 18≤n≤100$ we give corresponding lower bounds. Besides that a few preliminary structural results are obtained. For the related problem of the maximum possible number of isosceles right triangles we determine the exact values for n≤14 and give lower bounds for 15≤n≤50.

Further data

Item Type: Preprint, postprint
Keywords: Erdös problems; similar squares; isosceles right triangles; point sets; Euclidean plane
Subject classification: Mathematics Subject Classification Code: 52C10 (05C35)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 15 Jan 2022 22:00
Last Modified: 17 Jan 2022 06:28
URI: https://eref.uni-bayreuth.de/id/eprint/68388