On a Heilbronn-type problem

Diao Hansheng; Leng Gangsong; Si Lin

doi:10.1016/j.disc.2007.07.101

On a Heilbronn-type problem

Diao Hansheng, Leng Gangsong, Si Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.

Original language	English (US)
Pages (from-to)	3960-3981
Number of pages	22
Journal	Discrete Mathematics
Volume	308
Issue number	17
DOIs	https://doi.org/10.1016/j.disc.2007.07.101
State	Published - Sep 6 2008

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Keywords

Area
Convex figure
Heilbronn's problem
Parallelogram
Soifer's problem
Triangle

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10.1016/j.disc.2007.07.101

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title = "On a Heilbronn-type problem",

abstract = "Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.",

keywords = "Area, Convex figure, Heilbronn's problem, Parallelogram, Soifer's problem, Triangle",

author = "Diao Hansheng and Leng Gangsong and Si Lin",

note = "Funding Information: Supported by National Natural Sciences Foundation of China (No. 10671117). ",

year = "2008",

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doi = "10.1016/j.disc.2007.07.101",

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T1 - On a Heilbronn-type problem

AU - Hansheng, Diao

AU - Gangsong, Leng

AU - Lin, Si

N1 - Funding Information: Supported by National Natural Sciences Foundation of China (No. 10671117).

PY - 2008/9/6

Y1 - 2008/9/6

N2 - Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.

AB - Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.

KW - Area

KW - Convex figure

KW - Heilbronn's problem

KW - Parallelogram

KW - Soifer's problem

KW - Triangle

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DO - 10.1016/j.disc.2007.07.101

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JO - Discrete Mathematics

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On a Heilbronn-type problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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