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

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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 < 3 2 n  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 < 3 2 n 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.

  • [1]

    E. Ackerman , K. Buchin , C. Knauer , R. Pinchasi and G. Rote . There are not too many Magic Configurations. Discrete Comput. Geom., 39(1—3):316, 2008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2]

    R. Balasubramanian and P. P. Pandey . On a theorem of Deshouillers and Freiman. European J Combin. 70:284-296, 2018.

  • [3]

    R. Bix . Conics and Cubics: A Concrete Introduction to Algebraic Curves. Undergraduate Texts in Mathematics, 2nd edn. Springer, New York (2006).

    • Search Google Scholar
    • Export Citation
  • [4]

    A. Blokhuis , G. Marino and F. Mazzocca , Generalized hyperfocused arcs in PG(2, p). J. Combin. Des., 22(12):506-513, 2014.

  • [5]

    P. Erdős and G. Purdy . Some combinatorial problems in the plane. J. Combinatorial Theory, Ser. A, 25:205-210, 1978.

  • [6]

    G. A. Freiman . Groups and the inverse problems of additive number theory. Number-theoretic studies in the Markov spectrum and in the structural theory of set addition pp. 175-183. Kalinin. Gos. Univ., Moscow, (1973). In Russian.

    • Search Google Scholar
    • Export Citation
  • [7]

    B. Green and T. Tao . Onsets defining few ordinary lines. Discrete Comput. Geom., 50(2):409-468, 2013.

  • [8]

    R. E. Jamison . Few slopes without collinearity. Discrete Math., 60:199-206, 1986.

  • [9]

    R. Karasev . Residues and the combinatorial Nullstellensatz. Period. Math. Hungar., 78(2):157-165, 2019.

  • [10]

    Ch. Keller and R. Pinchasi . On sets of n points in general position that determine lines that can be pierced by n points. Discrete Comput. Geom., 64(2):382-385, 2020.

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    • Search Google Scholar
    • Export Citation
  • [11]

    V. F. Lev . Restricted set addition in groups. I. The classical setting. J. London Math. Soc. (2), 62(1):27-40, 2000.

  • [12]

    H. B. Mann . Addition theorems: The addition theorems of group theory and number theory. Interscience Publishers John Wiley & Sons New York-London-Sydney (1965).

    • Search Google Scholar
    • Export Citation
  • [13]

    L. Milicevic . Classification theorem for strong triangle blocking arrangements. Publ. Inst. Math. (Beograd) (N.S.), 107(121):1-36, 2020.

  • [14]

    U. S. R. Murty . How many magic configurations are there? American Mathematical Monthly, 78(9):1000-1002, (1971).

  • [15]

    C. Pilatte . On the sets of n points forming n +1 directions. Elec. J. of Combin., 27(1), 2020. See also: arXiv:1811.01055, 2018.

  • [16]

    C. Pilatte . Addendum to the paper “On the sets of n points forming n +1 directions”. arXiv preprint arXiv:1811.01055, 2021.

  • [17]

    R. Pinchasi and A. Polyanskii . A one-page solution of a problem of Erdős and Purdy. Discrete Comput. Geom, 64(2):382-385, 2020.

  • [18]

    P. R. Scott . On the sets of directions determined by n points. Amer Math. Monthly, 77:502-505, 1970.

  • [19]

    P. Ungar . 2n noncollinear points determine at least 2n directions. J. Combin. Theory, Ser. A, 33:343-347, 1982.

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Editors in Chief

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András STIPSICZ (Rényi Institute of Mathematics)
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STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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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
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