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References

Full bibliographic data for everything cited on this site. The verification trail (which statements were read in the original papers) is in the repository file notes/literature_followup.md.

Classical theorems on real arrangements

  1. N. G. de Bruijn, P. Erdős, On a combinatorial problem, Indagationes Mathematicae 10 (1948), 421–423 (= Proc. Kon. Ned. Akad. Wetensch. 51 (1948), 1277–1279).
  2. E. Melchior, Über Vielseite der projektiven Ebene, Deutsche Mathematik 5 (1940/41), 461–475.
  3. L. M. Kelly, W. O. J. Moser, On the number of ordinary lines determined by n points, Canadian Journal of Mathematics 10 (1958), 210–219. doi:10.4153/CJM-1958-024-6
  4. P. D. T. A. Elliott, On the number of circles determined by n points, Acta Mathematica Academiae Scientiarum Hungaricae 18 (1967), 181–188. doi:10.1007/BF02020972
  5. J. Csima, E. T. Sawyer, There exist 6n/13 ordinary points, Discrete & Computational Geometry 9 (1993), 187–202. doi:10.1007/BF02189318
  6. F. Hirzebruch, Arrangements of lines and algebraic surfaces, in: Arithmetic and Geometry, Vol. II (M. Artin, J. Tate, eds.), Progress in Mathematics 36, Birkhäuser, Boston, 1983, 113–140. doi:10.1007/978-1-4757-9286-7_7
  7. P. Pokora, Hirzebruch-type inequalities viewed as tools in combinatorics, Electronic Journal of Combinatorics 28 (1) (2021), P1.9. doi:10.37236/8335
  8. B. Green, T. Tao, On sets defining few ordinary lines, Discrete & Computational Geometry 50 (2013), 409–468. doi:10.1007/s00454-013-9518-9, arXiv:1208.4714
  9. J. Beck, On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry, Combinatorica 3 (1983), 281–297. doi:10.1007/BF02579184

Grünbaum's problem on the number of intersection points

  1. B. Grünbaum, Arrangements and Spreads, CBMS Regional Conference Series in Mathematics 10, American Mathematical Society, Providence, RI, 1972.
  2. P. Erdős, On a problem of Grünbaum, Canadian Mathematical Bulletin 15 (1972), 23–25. doi:10.4153/CMB-1972-005-4
  3. P. Salamon, P. Erdős, The solution to a problem of Grünbaum, Canadian Mathematical Bulletin 31 (1988), 129–138. doi:10.4153/CMB-1988-020-2
  4. P. Erdős, G. Purdy, Extremal problems in combinatorial geometry, in: Handbook of Combinatorics, Vol. 1 (R. L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam, 1995, 809–874.

The orchard problem

  1. J. J. Sylvester, Problem 2473, Mathematical Questions and Solutions from the Educational Times 8 (1867), 106–107.
  2. S. A. Burr, B. Grünbaum, N. J. A. Sloane, The orchard problem, Geometriae Dedicata 2 (1974), 397–424. doi:10.1007/BF00147569
  3. Z. Füredi, I. Palásti, Arrangements of lines with a large number of triangles, Proceedings of the American Mathematical Society 92 (1984), 561–566. doi:10.1090/S0002-9939-1984-0760946-2

Configurations and oriented matroids

  1. D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination, Chelsea, New York, 1952 (German original Anschauliche Geometrie, Springer, Berlin, 1932), Chapter III.
  2. H. S. M. Coxeter, A problem of collinear points, American Mathematical Monthly 55 (1948), 26–28.
  3. H. Gropp, Configurations and their realization, Discrete Mathematics 174 (1997), 137–151. doi:10.1016/S0012-365X(96)00327-5
  4. B. Grünbaum, Configurations of Points and Lines, Graduate Studies in Mathematics 103, American Mathematical Society, Providence, RI, 2009.
  5. M. Artebani, I. Dolgachev, The Hesse pencil of plane cubic curves, L'Enseignement Mathématique 55 (2009), 235–273.
  6. J. Folkman, J. Lawrence, Oriented matroids, Journal of Combinatorial Theory, Series B 25 (1978), 199–236. doi:10.1016/0095-8956(78)90039-4
  7. A. Björner, M. Las Vergnas, B. Sturmfels, N. White, G. M. Ziegler, Oriented Matroids, 2nd ed., Encyclopedia of Mathematics and its Applications 46, Cambridge University Press, 1999. doi:10.1017/CBO9780511586507
  8. J. Bokowski, P. Pokora, On line and pseudoline configurations and ball-quotients, Periodica Mathematica Hungarica 77 (2018), 164–174. doi:10.1007/s10998-017-0224-x

Linear spaces

  1. A. Betten, D. Betten, Linear spaces with at most 12 points, Journal of Combinatorial Designs 7 (1999), 119–145.
  2. M. Barakat, R. Behrends, C. Jefferson, L. Kühne, M. Leuner, On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture, SIAM Journal on Discrete Mathematics 35 (2021). arXiv:1907.01073
  3. C. J. Colbourn, A. Rosa, Triple Systems, Oxford University Press, 1999 (uniqueness of the Steiner triple system of order 9).

Partitions

  1. G. H. Hardy, S. Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society (2) 17 (1918), 75–115.
  2. E. M. Wright, Asymptotic partition formulae III. Partitions into k-th powers, Acta Mathematica 63 (1934), 143–191.

OEIS entries

  • A072964 Number of partitions of the n-th triangular number into triangular parts.
  • A003035 Maximal number of 3-tree rows in n-tree orchard problem.
  • A003034 Sylvester's problem: minimal number of ordinary lines through n points in the plane.
  • A001200 Number of linear geometries on n (unlabeled) points.
  • A048872, A132346 Non-isomorphic arrangements of n lines in the real projective plane.
  • A129230, A005834 Sequences that coincide with ours on a few terms only.

Software

  • A. Biere, K. Fazekas, M. Fleury, M. Heisinger, CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling entering the SAT Competition 2020, in: Proc. SAT Competition 2020, University of Helsinki, 2020, 51–53. Used as CaDiCaL 1.9.5.
  • A. Ignatiev, A. Morgado, J. Marques-Silva, PySAT: a Python toolkit for prototyping with SAT oracles, in: SAT 2018, Lecture Notes in Computer Science 10929, Springer, 2018, 428–437. doi:10.1007/978-3-319-94144-8_26
  • MkDocs with the Material theme; MathJax.