No-three-in-line problem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "No-three-in-line problem" in English language version.

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Brass, Moser & Pach 2005. Brass, Peter; Moser, William; Pach, János (2005). "Section 10.1: Packing lattice points in subspaces". Research Problems in Discrete Geometry. Springer, New York. pp. 417–421. ISBN 978-0-387-29929-7. MR 2163782.
Craggs & Hughes-Jones 1976; Kløve 1978, 1979; Anderson 1979; Harborth, Oertel & Prellberg 1989; Flammenkamp 1992, 1998. Craggs, D.; Hughes-Jones, R. (1976). "On the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 20 (3): 363–364. doi:10.1016/0097-3165(76)90030-3. MR 0406804. Kløve, Torleiv (1978). "On the no-three-in-line problem. II". Journal of Combinatorial Theory. Series A. 24 (1): 126–127. doi:10.1016/0097-3165(78)90053-5. MR 0462998. Kløve, Torleiv (1979). "On the no-three-in-line problem. III". Journal of Combinatorial Theory. Series A. 26 (1): 82–83. doi:10.1016/0097-3165(79)90055-4. MR 0525088. Anderson, David Brent (1979). "Update on the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 27 (3): 365–366. doi:10.1016/0097-3165(79)90025-6. MR 0555806. Harborth, Heiko; Oertel, Philipp; Prellberg, Thomas (1989). "No-three-in-line for seventeen and nineteen". Proceedings of the Oberwolfach Meeting “Kombinatorik” (1986). Discrete Mathematics. 73 (1–2): 89–90. doi:10.1016/0012-365X(88)90135-5. MR 0974815. Flammenkamp, Achim (1992). "Progress in the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 60 (2): 305–311. doi:10.1016/0097-3165(92)90012-J. Flammenkamp, Achim (1998). "Progress in the no-three-in-line problem, II". Journal of Combinatorial Theory. Series A. 81 (1): 108–113. doi:10.1006/jcta.1997.2829.
Guy & Kelly 1968. Guy, R. K.; Kelly, P. A. (1968). "The no-three-in-line problem". Canadian Mathematical Bulletin. 11 (4): 527–531. doi:10.4153/CMB-1968-062-3. MR 0238765.
Brass et al. 2007. Brass, Peter; Cenek, Eowyn; Duncan, Christian A.; Efrat, Alon; Erten, Cesim; Ismailescu, Dan P.; Kobourov, Stephen G.; Lubiw, Anna; Mitchell, Joseph S. B. (2007). "On simultaneous planar graph embeddings". Computational Geometry. 36 (2): 117–130. doi:10.1016/j.comgeo.2006.05.006. MR 2278011.
Komlós, Pintz & Szemerédi 1982. Komlós, J.; Pintz, J.; Szemerédi, E. (1982). "A lower bound for Heilbronn's problem". Journal of the London Mathematical Society. 25 (1): 13–24. doi:10.1112/jlms/s2-25.1.13. MR 0645860.
Froese et al. 2017; Eppstein 2018 Froese, Vincent; Kanj, Iyad; Nichterlein, André; Niedermeier, Rolf (2017). "Finding points in general position". International Journal of Computational Geometry & Applications. 27 (4): 277–296. arXiv:1508.01097. doi:10.1142/S021819591750008X. MR 3766097. S2CID 47260245. Eppstein, David (2018). "Chapter 9: General position". Forbidden Configurations in Discrete Geometry. Cambridge University Press. pp. 72–86.
Payne & Wood 2013. Payne, Michael S.; Wood, David R. (2013). "On the general position subset selection problem". SIAM Journal on Discrete Mathematics. 27 (4): 1727–1733. arXiv:1208.5289. doi:10.1137/120897493. MR 3111653. S2CID 7164626.
Elkin 2011. Elkin, Michael (2011). "An improved construction of progression-free sets". Israel Journal of Mathematics. 184: 93–128. arXiv:0801.4310. doi:10.1007/s11856-011-0061-1. MR 2823971.
Jarník 1926. Jarník, Vojtěch (1926). "Über die Gitterpunkte auf konvexen Kurven" [On the grid points on convex curves]. Mathematische Zeitschrift (in German). 24 (1): 500–518. doi:10.1007/BF01216795. MR 1544776. S2CID 117747514.
Misiak et al. 2016. Misiak, Aleksander; Stępień, Zofia; Szymaszkiewicz, Alicja; Szymaszkiewicz, Lucjan; Zwierzchowski, Maciej (2016). "A note on the no-three-in-line problem on a torus". Discrete Mathematics. 339 (1): 217–221. arXiv:1406.6713. doi:10.1016/j.disc.2015.08.006. MR 3404483. S2CID 40210322.
Cooper & Solymosi 2005. Cooper, Joshua N.; Solymosi, József (2005). "Collinear points in permutations" (PDF). Annals of Combinatorics. 9 (2): 169–175. arXiv:math/0408396. doi:10.1007/s00026-005-0248-4. MR 2153735. S2CID 11035679.
Ku & Wong 2018. Ku, Cheng Yeaw; Wong, Kok Bin (2018). "On no-three-in-line problem on $m$ -dimensional torus". Graphs and Combinatorics. 34 (2): 355–364. doi:10.1007/s00373-018-1878-8. MR 3774457. S2CID 3935268.

archive.org

Dudeney 1917. Dudeney, Henry (1917). "317. A puzzle with pawns". Amusements in Mathematics. Edinburgh: Nelson. p. 94. Solution, p. 222. Originally published in the London Tribune, November 7, 1906.

arxiv.org

Froese et al. 2017; Eppstein 2018 Froese, Vincent; Kanj, Iyad; Nichterlein, André; Niedermeier, Rolf (2017). "Finding points in general position". International Journal of Computational Geometry & Applications. 27 (4): 277–296. arXiv:1508.01097. doi:10.1142/S021819591750008X. MR 3766097. S2CID 47260245. Eppstein, David (2018). "Chapter 9: General position". Forbidden Configurations in Discrete Geometry. Cambridge University Press. pp. 72–86.
Payne & Wood 2013. Payne, Michael S.; Wood, David R. (2013). "On the general position subset selection problem". SIAM Journal on Discrete Mathematics. 27 (4): 1727–1733. arXiv:1208.5289. doi:10.1137/120897493. MR 3111653. S2CID 7164626.
Cooper et al. 2014. Cooper, Alec S.; Pikhurko, Oleg; Schmitt, John R.; Warrington, Gregory S. (2014). "Martin Gardner's minimum no-3-in-a-line problem". American Mathematical Monthly. 121 (3): 213–221. arXiv:1206.5350. doi:10.4169/amer.math.monthly.121.03.213. JSTOR 10.4169/amer.math.monthly.121.03.213. S2CID 887220.
Aichholzer, Eppstein & Hainzl (2023). Aichholzer, Oswin; Eppstein, David; Hainzl, Eva-Maria (January 2023). "Geometric dominating sets – a minimum version of the No-Three-In-Line Problem". Computational Geometry. 108. Elsevier: 101913. arXiv:2203.13170. doi:10.1016/j.comgeo.2022.101913. S2CID 249687906.
Pach, Thiele & Tóth 1998; Dujmović, Morin & Wood 2005; Di Giacomo, Liotta & Meijer 2005 Pach, János; Thiele, Torsten; Tóth, Géza (1998). "Three-dimensional grid drawings of graphs". Graph Drawing, 5th Int. Symp., GD '97. Lecture Notes in Computer Science. Vol. 1353. Springer-Verlag. pp. 47–51. doi:10.1007/3-540-63938-1_49. Dujmović, Vida; Morin, Pat; Wood, David R. (2005). "Layout of graphs with bounded tree-width". SIAM Journal on Computing. 34 (3): 553–579. arXiv:cs/0406024. doi:10.1137/S0097539702416141. S2CID 3264071. Di Giacomo, Emilio; Liotta, Giuseppe; Meijer, Henk (2005). "Computing straight-line 3d grid drawings of graphs in linear volume". Computational Geometry: Theory and Applications. 32 (1): 26–58. doi:10.1016/j.comgeo.2004.11.003.
Elkin 2011. Elkin, Michael (2011). "An improved construction of progression-free sets". Israel Journal of Mathematics. 184: 93–128. arXiv:0801.4310. doi:10.1007/s11856-011-0061-1. MR 2823971.
Misiak et al. 2016. Misiak, Aleksander; Stępień, Zofia; Szymaszkiewicz, Alicja; Szymaszkiewicz, Lucjan; Zwierzchowski, Maciej (2016). "A note on the no-three-in-line problem on a torus". Discrete Mathematics. 339 (1): 217–221. arXiv:1406.6713. doi:10.1016/j.disc.2015.08.006. MR 3404483. S2CID 40210322.
Cooper & Solymosi 2005. Cooper, Joshua N.; Solymosi, József (2005). "Collinear points in permutations" (PDF). Annals of Combinatorics. 9 (2): 169–175. arXiv:math/0408396. doi:10.1007/s00026-005-0248-4. MR 2153735. S2CID 11035679.

books.google.com

Brass, Moser & Pach 2005. Brass, Peter; Moser, William; Pach, János (2005). "Section 10.1: Packing lattice points in subspaces". Research Problems in Discrete Geometry. Springer, New York. pp. 417–421. ISBN 978-0-387-29929-7. MR 2163782.

doi.org

Craggs & Hughes-Jones 1976; Kløve 1978, 1979; Anderson 1979; Harborth, Oertel & Prellberg 1989; Flammenkamp 1992, 1998. Craggs, D.; Hughes-Jones, R. (1976). "On the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 20 (3): 363–364. doi:10.1016/0097-3165(76)90030-3. MR 0406804. Kløve, Torleiv (1978). "On the no-three-in-line problem. II". Journal of Combinatorial Theory. Series A. 24 (1): 126–127. doi:10.1016/0097-3165(78)90053-5. MR 0462998. Kløve, Torleiv (1979). "On the no-three-in-line problem. III". Journal of Combinatorial Theory. Series A. 26 (1): 82–83. doi:10.1016/0097-3165(79)90055-4. MR 0525088. Anderson, David Brent (1979). "Update on the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 27 (3): 365–366. doi:10.1016/0097-3165(79)90025-6. MR 0555806. Harborth, Heiko; Oertel, Philipp; Prellberg, Thomas (1989). "No-three-in-line for seventeen and nineteen". Proceedings of the Oberwolfach Meeting “Kombinatorik” (1986). Discrete Mathematics. 73 (1–2): 89–90. doi:10.1016/0012-365X(88)90135-5. MR 0974815. Flammenkamp, Achim (1992). "Progress in the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 60 (2): 305–311. doi:10.1016/0097-3165(92)90012-J. Flammenkamp, Achim (1998). "Progress in the no-three-in-line problem, II". Journal of Combinatorial Theory. Series A. 81 (1): 108–113. doi:10.1006/jcta.1997.2829.
Flammenkamp 1992, 1998. Flammenkamp, Achim (1992). "Progress in the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 60 (2): 305–311. doi:10.1016/0097-3165(92)90012-J. Flammenkamp, Achim (1998). "Progress in the no-three-in-line problem, II". Journal of Combinatorial Theory. Series A. 81 (1): 108–113. doi:10.1006/jcta.1997.2829.
Erdős did not publish this observation; it appears in Roth 1951. Roth, K. F. (1951). "On a problem of Heilbronn". Journal of the London Mathematical Society. 26 (3): 198–204. doi:10.1112/jlms/s1-26.3.198.
Hall et al. 1975. Hall, R. R.; Jackson, T. H.; Sudbery, A.; Wild, K. (1975). "Some advances in the no-three-in-line problem". Journal of Combinatorial Theory. Series A. 18 (3): 336–341. doi:10.1016/0097-3165(75)90043-6.
Guy & Kelly 1968. Guy, R. K.; Kelly, P. A. (1968). "The no-three-in-line problem". Canadian Mathematical Bulletin. 11 (4): 527–531. doi:10.4153/CMB-1968-062-3. MR 0238765.
Brass et al. 2007. Brass, Peter; Cenek, Eowyn; Duncan, Christian A.; Efrat, Alon; Erten, Cesim; Ismailescu, Dan P.; Kobourov, Stephen G.; Lubiw, Anna; Mitchell, Joseph S. B. (2007). "On simultaneous planar graph embeddings". Computational Geometry. 36 (2): 117–130. doi:10.1016/j.comgeo.2006.05.006. MR 2278011.
Wood 2005. Wood, David R. (2005). "Grid drawings of $k$ -colourable graphs". Computational Geometry: Theory and Applications. 30 (1): 25–28. doi:10.1016/j.comgeo.2004.06.001.
Roth 1951. Roth, K. F. (1951). "On a problem of Heilbronn". Journal of the London Mathematical Society. 26 (3): 198–204. doi:10.1112/jlms/s1-26.3.198.
Komlós, Pintz & Szemerédi 1982. Komlós, J.; Pintz, J.; Szemerédi, E. (1982). "A lower bound for Heilbronn's problem". Journal of the London Mathematical Society. 25 (1): 13–24. doi:10.1112/jlms/s2-25.1.13. MR 0645860.
Froese et al. 2017; Eppstein 2018 Froese, Vincent; Kanj, Iyad; Nichterlein, André; Niedermeier, Rolf (2017). "Finding points in general position". International Journal of Computational Geometry & Applications. 27 (4): 277–296. arXiv:1508.01097. doi:10.1142/S021819591750008X. MR 3766097. S2CID 47260245. Eppstein, David (2018). "Chapter 9: General position". Forbidden Configurations in Discrete Geometry. Cambridge University Press. pp. 72–86.
Payne & Wood 2013. Payne, Michael S.; Wood, David R. (2013). "On the general position subset selection problem". SIAM Journal on Discrete Mathematics. 27 (4): 1727–1733. arXiv:1208.5289. doi:10.1137/120897493. MR 3111653. S2CID 7164626.
Cooper et al. 2014. Cooper, Alec S.; Pikhurko, Oleg; Schmitt, John R.; Warrington, Gregory S. (2014). "Martin Gardner's minimum no-3-in-a-line problem". American Mathematical Monthly. 121 (3): 213–221. arXiv:1206.5350. doi:10.4169/amer.math.monthly.121.03.213. JSTOR 10.4169/amer.math.monthly.121.03.213. S2CID 887220.
Aichholzer, Eppstein & Hainzl (2023). Aichholzer, Oswin; Eppstein, David; Hainzl, Eva-Maria (January 2023). "Geometric dominating sets – a minimum version of the No-Three-In-Line Problem". Computational Geometry. 108. Elsevier: 101913. arXiv:2203.13170. doi:10.1016/j.comgeo.2022.101913. S2CID 249687906.
Pór & Wood 2007. Pór, Attila; Wood, David R. (2007). "No-three-in-line-in-3D". Algorithmica. 47 (4): 481. doi:10.1007/s00453-006-0158-9. S2CID 209841346.
Pach, Thiele & Tóth 1998; Dujmović, Morin & Wood 2005; Di Giacomo, Liotta & Meijer 2005 Pach, János; Thiele, Torsten; Tóth, Géza (1998). "Three-dimensional grid drawings of graphs". Graph Drawing, 5th Int. Symp., GD '97. Lecture Notes in Computer Science. Vol. 1353. Springer-Verlag. pp. 47–51. doi:10.1007/3-540-63938-1_49. Dujmović, Vida; Morin, Pat; Wood, David R. (2005). "Layout of graphs with bounded tree-width". SIAM Journal on Computing. 34 (3): 553–579. arXiv:cs/0406024. doi:10.1137/S0097539702416141. S2CID 3264071. Di Giacomo, Emilio; Liotta, Giuseppe; Meijer, Henk (2005). "Computing straight-line 3d grid drawings of graphs in linear volume". Computational Geometry: Theory and Applications. 32 (1): 26–58. doi:10.1016/j.comgeo.2004.11.003.
Elkin 2011. Elkin, Michael (2011). "An improved construction of progression-free sets". Israel Journal of Mathematics. 184: 93–128. arXiv:0801.4310. doi:10.1007/s11856-011-0061-1. MR 2823971.
Jarník 1926. Jarník, Vojtěch (1926). "Über die Gitterpunkte auf konvexen Kurven" [On the grid points on convex curves]. Mathematische Zeitschrift (in German). 24 (1): 500–518. doi:10.1007/BF01216795. MR 1544776. S2CID 117747514.
Misiak et al. 2016. Misiak, Aleksander; Stępień, Zofia; Szymaszkiewicz, Alicja; Szymaszkiewicz, Lucjan; Zwierzchowski, Maciej (2016). "A note on the no-three-in-line problem on a torus". Discrete Mathematics. 339 (1): 217–221. arXiv:1406.6713. doi:10.1016/j.disc.2015.08.006. MR 3404483. S2CID 40210322.
Cooper & Solymosi 2005. Cooper, Joshua N.; Solymosi, József (2005). "Collinear points in permutations" (PDF). Annals of Combinatorics. 9 (2): 169–175. arXiv:math/0408396. doi:10.1007/s00026-005-0248-4. MR 2153735. S2CID 11035679.
Ku & Wong 2018. Ku, Cheng Yeaw; Wong, Kok Bin (2018). "On no-three-in-line problem on $m$ -dimensional torus". Graphs and Combinatorics. 34 (2): 355–364. doi:10.1007/s00373-018-1878-8. MR 3774457. S2CID 3935268.

eudml.org

Jarník 1926. Jarník, Vojtěch (1926). "Über die Gitterpunkte auf konvexen Kurven" [On the grid points on convex curves]. Mathematische Zeitschrift (in German). 24 (1): 500–518. doi:10.1007/BF01216795. MR 1544776. S2CID 117747514.

jstor.org

Gardner 1976. Gardner, Martin (October 1976). "Combinatorial problems, some old, some new and all newly attacked by computer". Mathematical Games. Scientific American. Vol. 235, no. 4. pp. 131–137. JSTOR 24950467.
Cooper et al. 2014. Cooper, Alec S.; Pikhurko, Oleg; Schmitt, John R.; Warrington, Gregory S. (2014). "Martin Gardner's minimum no-3-in-a-line problem". American Mathematical Monthly. 121 (3): 213–221. arXiv:1206.5350. doi:10.4169/amer.math.monthly.121.03.213. JSTOR 10.4169/amer.math.monthly.121.03.213. S2CID 887220.

mathpuzzle.com

As reported by Pegg 2005. The discovery of this error was credited by Pegg to Gabor Ellmann. Pegg, Ed Jr. (April 11, 2005). "Chessboard Tasks". Math Games. Mathematical Association of America. Retrieved June 25, 2012.

quantamagazine.org

Klarreich 2016. Klarreich, Erica (May 31, 2016). "Simple Set Game Proof Stuns Mathematicians". Quanta.

sc.edu

people.math.sc.edu

Cooper & Solymosi 2005. Cooper, Joshua N.; Solymosi, József (2005). "Collinear points in permutations" (PDF). Annals of Combinatorics. 9 (2): 169–175. arXiv:math/0408396. doi:10.1007/s00026-005-0248-4. MR 2153735. S2CID 11035679.

semanticscholar.org

api.semanticscholar.org

Froese et al. 2017; Eppstein 2018 Froese, Vincent; Kanj, Iyad; Nichterlein, André; Niedermeier, Rolf (2017). "Finding points in general position". International Journal of Computational Geometry & Applications. 27 (4): 277–296. arXiv:1508.01097. doi:10.1142/S021819591750008X. MR 3766097. S2CID 47260245. Eppstein, David (2018). "Chapter 9: General position". Forbidden Configurations in Discrete Geometry. Cambridge University Press. pp. 72–86.
Payne & Wood 2013. Payne, Michael S.; Wood, David R. (2013). "On the general position subset selection problem". SIAM Journal on Discrete Mathematics. 27 (4): 1727–1733. arXiv:1208.5289. doi:10.1137/120897493. MR 3111653. S2CID 7164626.
Cooper et al. 2014. Cooper, Alec S.; Pikhurko, Oleg; Schmitt, John R.; Warrington, Gregory S. (2014). "Martin Gardner's minimum no-3-in-a-line problem". American Mathematical Monthly. 121 (3): 213–221. arXiv:1206.5350. doi:10.4169/amer.math.monthly.121.03.213. JSTOR 10.4169/amer.math.monthly.121.03.213. S2CID 887220.
Aichholzer, Eppstein & Hainzl (2023). Aichholzer, Oswin; Eppstein, David; Hainzl, Eva-Maria (January 2023). "Geometric dominating sets – a minimum version of the No-Three-In-Line Problem". Computational Geometry. 108. Elsevier: 101913. arXiv:2203.13170. doi:10.1016/j.comgeo.2022.101913. S2CID 249687906.
Pór & Wood 2007. Pór, Attila; Wood, David R. (2007). "No-three-in-line-in-3D". Algorithmica. 47 (4): 481. doi:10.1007/s00453-006-0158-9. S2CID 209841346.
Pach, Thiele & Tóth 1998; Dujmović, Morin & Wood 2005; Di Giacomo, Liotta & Meijer 2005 Pach, János; Thiele, Torsten; Tóth, Géza (1998). "Three-dimensional grid drawings of graphs". Graph Drawing, 5th Int. Symp., GD '97. Lecture Notes in Computer Science. Vol. 1353. Springer-Verlag. pp. 47–51. doi:10.1007/3-540-63938-1_49. Dujmović, Vida; Morin, Pat; Wood, David R. (2005). "Layout of graphs with bounded tree-width". SIAM Journal on Computing. 34 (3): 553–579. arXiv:cs/0406024. doi:10.1137/S0097539702416141. S2CID 3264071. Di Giacomo, Emilio; Liotta, Giuseppe; Meijer, Henk (2005). "Computing straight-line 3d grid drawings of graphs in linear volume". Computational Geometry: Theory and Applications. 32 (1): 26–58. doi:10.1016/j.comgeo.2004.11.003.
Jarník 1926. Jarník, Vojtěch (1926). "Über die Gitterpunkte auf konvexen Kurven" [On the grid points on convex curves]. Mathematische Zeitschrift (in German). 24 (1): 500–518. doi:10.1007/BF01216795. MR 1544776. S2CID 117747514.
Misiak et al. 2016. Misiak, Aleksander; Stępień, Zofia; Szymaszkiewicz, Alicja; Szymaszkiewicz, Lucjan; Zwierzchowski, Maciej (2016). "A note on the no-three-in-line problem on a torus". Discrete Mathematics. 339 (1): 217–221. arXiv:1406.6713. doi:10.1016/j.disc.2015.08.006. MR 3404483. S2CID 40210322.
Cooper & Solymosi 2005. Cooper, Joshua N.; Solymosi, József (2005). "Collinear points in permutations" (PDF). Annals of Combinatorics. 9 (2): 169–175. arXiv:math/0408396. doi:10.1007/s00026-005-0248-4. MR 2153735. S2CID 11035679.
Ku & Wong 2018. Ku, Cheng Yeaw; Wong, Kok Bin (2018). "On no-three-in-line problem on $m$ -dimensional torus". Graphs and Combinatorics. 34 (2): 355–364. doi:10.1007/s00373-018-1878-8. MR 3774457. S2CID 3935268.

stanford.edu

www-cs-faculty.stanford.edu

The Weekly Dispatch, April 29 and May 13, 1900, as cited by Knuth 2008. Knuth, Donald E. (2008). "Answer to exercise 242". The Art of Computer Programming, Fascicle 1b: A Draft of Section 7.1.4: Binary Decision Diagrams. p. 130.