Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 3-4

On Sets of Points in General Position That Lie on a Cubic Curve in the Plane

Authors:
Mehdi Makhul Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria

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and
Rom Pinchasi Mathematics Department, Technion - Israel Institute of Technology, Haifa 32000, Israel

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Pages:
196–208
Online Publication Date:
16 Aug 2022
Publication Date:
14 Dec 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01527
Keywords:
cubic curves; points; lines; elliptic curves
Restricted access

Let P be a set of n points in general position in the plane. Let R be a set of points disjoint from P such that for every x, y € P the line through x and y contains a point in R. We show that if R<32n and P∪R is contained in a cubic curve c in the plane, then P has a special property with respect to the natural group structure on c. That is, P is contained in a coset of a subgroup H of c of cardinality at most |R|.

We use the same approach to show a similar result in the case where each of B and G is a set of n points in general position in the plane and every line through a point in B and a point in G passes through a point in R. This provides a partial answer to a problem of Karasev.

The bound R<32n is best possible at least for part of our results. Our extremal constructions provide a counterexample to an old conjecture attributed to Jamison about point sets that determine few directions.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

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Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
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  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
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STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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2022  
Web of Science  
Total Cites
WoS		 570
Journal Impact Factor 0.7
Rank by Impact Factor

Mathematics (Q3)
Impact Factor
without
Journal Self Cites		 0.7
5 Year
Impact Factor		 0.8
Journal Citation Indicator 0.65
Rank by Journal Citation Indicator

Mathematics (Q2)
Scimago  
Scimago
H-index		 26
Scimago
Journal Rank		 0.351
Scimago Quartile Score

Mathematics (Q3)
Scopus  
Scopus
Cite Score		 1.8
Scopus
CIte Score Rank		 General Mathematics 128/387 (67th PCTL)
Scopus
SNIP		 1.276

2021  
Web of Science  
Total Cites
WoS		 589
Journal Impact Factor 0,739
Rank by Impact Factor Mathematics 229/332
Impact Factor
without
Journal Self Cites		 0,710
5 Year
Impact Factor		 0,654
Journal Citation Indicator 0,57
Rank by Journal Citation Indicator Mathematics 287/474
Scimago  
Scimago
H-index		 26
Scimago
Journal Rank		 0,265
Scimago Quartile Score Mathematics (miscellaneous) (Q3)
Scopus  
Scopus
Cite Score		 1,3
Scopus
CIte Score Rank		 General Mathematics 193/391 (Q2)
Scopus
SNIP		 0,746

2020  
Total Cites 536
WoS
Journal
Impact Factor		 0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
submission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS		 463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites		 0,468
5 Year
Impact Factor		 0,413
Immediacy
Index		 0,135
Citable
Items		 37
Total
Articles		 37
Total
Reviews		 0
Cited
Half-Life		 21,4
Citing
Half-Life		 15,5
Eigenfactor
Score		 0,00039
Article Influence
Score		 0,196
% Articles
in
Citable Items		 100,00
Normalized
Eigenfactor		 0,04841
Average
IF
Percentile		 13,117
Scimago
H-index		 23
Scimago
Journal Rank		 0,234
Scopus
Scite Score		 76/104=0,7
Scopus
Scite Score Rank		 General Mathematics 247/368 (Q3)
Scopus
SNIP		 0,671
Acceptance
Rate		 14%

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
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Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
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ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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