Sylvester–Gallai theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Sylvester–Gallai theorem" in English language version.

refsWebsite

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17ams.org

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16doi.org

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8semanticscholar.org

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5jstor.org

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4arxiv.org

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3projecteuclid.org

3,707^th place

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1math-inst.hu

low place

1web.archive.org

1^st place

1uwaterloo.ca

3,153^rd place

2,332^nd place

1acm.org

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840^th place

1washington.edu

1,067^th place

749^th place

acm.org (Global: 1,185^th place; English: 840^th place)

dl.acm.org

Lenchner (2008). Lenchner, Jonathan (2008). Sylvester-Gallai results and other contributions to combinatorial and computational geometry (Ph.D. Thesis).

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Elkies, Pretorius & Swanepoel (2006). Elkies, Noam; Pretorius, Lou M.; Swanepoel, Konrad J. (2006), "Sylvester–Gallai theorems for complex numbers and quaternions", Discrete & Computational Geometry, 35 (3): 361–373, arXiv:math/0403023, doi:10.1007/s00454-005-1226-7, MR 2202107, S2CID 1647360
Borwein & Moser (1990). Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations", Aequationes Mathematicae, 40 (1): 111–135, doi:10.1007/BF02112289, MR 1069788, S2CID 122052678
Steinberg et al. (1944); Erdős (1982). Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021 Erdős, P. (1982), "Personal reminiscences and remarks on the mathematical work of Tibor Gallai" (PDF), Combinatorica, 2 (3): 207–212, doi:10.1007/BF02579228, MR 0698647, S2CID 1135308
MR 0041447
MR 0056941
Shephard (1968). Shephard, G. C. (1968), "Twenty problems on convex polyhedra, part I", The Mathematical Gazette, 52 (380): 136–156, doi:10.2307/3612678, JSTOR 3612678, MR 0231278, S2CID 250442107
Aigner & Ziegler (2018); Pambuccian (2009). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973
Coxeter (1948); Pambuccian (2009). For Steinberg's proof see Steinberg et al. (1944). Coxeter, H. S. M. (1948), "A problem of collinear points", American Mathematical Monthly, 55 (1): 26–28, doi:10.2307/2305324, JSTOR 2305324, MR 0024137 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Mandelkern (2016). Mandelkern, Mark (2016), "A constructive version of the Sylvester–Gallai theorem", Acta Mathematica Hungarica, 150: 121–130, arXiv:2402.03662, doi:10.1007/s10474-016-0624-z, MR 3542040, S2CID 124023963
Mukhopadhyay & Greene (2012). Mukhopadhyay, Asish; Greene, Eugene (2012), "The ordinary line problem revisited", Computational Geometry: Theory and Applications, 45 (3): 127–130, doi:10.1016/j.comgeo.2011.10.003, MR 2853475
Crowe & McKee (1968). Crowe, D. W.; McKee, T. A. (1968), "Sylvester's problem on collinear points", Mathematics Magazine, 41 (1): 30–34, doi:10.2307/2687957, JSTOR 2687957, MR 0235452
Geelen, Gerards & Kapoor (2000). Geelen, J. F.; Gerards, A. M. H.; Kapoor, A. (2000), "The excluded minors for GF(4)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 79 (2): 247–299, doi:10.1006/jctb.2000.1963, MR 1769191, archived from the original (PDF) on 2010-09-24
Beck (1983). Beck, József (1983), "On the lattice property of the plane and some problems of Dirac, Motzkin, and Erdős in combinatorial geometry", Combinatorica, 3 (3–4): 281–297, doi:10.1007/BF02579184, MR 0729781, S2CID 31011939
Green & Tao (2013). Green, Ben; Tao, Terence (2013), "On sets defining few ordinary lines", Discrete & Computational Geometry, 50 (2): 409–468, arXiv:1208.4714, doi:10.1007/s00454-013-9518-9, MR 3090525, S2CID 15813230
For the history of this variation of the problem, see also Grünbaum (1999) Grünbaum, Branko (1999), "Monochromatic intersection points in families of colored lines" (PDF), Geombinatorics, 9 (1): 3–9, MR 1698297
Basit et al. (2019). Basit, Abdul; Dvir, Zeev; Saraf, Shubhangi; Wolf, Charles (2019), "On the number of ordinary lines determined by sets in complex space", Discrete & Computational Geometry, 61 (4): 778–808, arXiv:1611.08740, doi:10.1007/s00454-018-0039-4, MR 3943495, S2CID 125616042
Chvátal (2004); Chen (2006); Pambuccian (2009) Chvátal, Vašek (2004), "Sylvester–Gallai theorem and metric betweenness", Discrete & Computational Geometry, 31 (2): 175–195, doi:10.1007/s00454-003-0795-6, MR 2060634 Chen, Xiaomin (2006), "The Sylvester–Chvátal theorem", Discrete & Computational Geometry, 35 (2): 193–199, doi:10.1007/s00454-005-1216-9, MR 2195050 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973

arxiv.org (Global: 69^th place; English: 59^th place)

Elkies, Pretorius & Swanepoel (2006). Elkies, Noam; Pretorius, Lou M.; Swanepoel, Konrad J. (2006), "Sylvester–Gallai theorems for complex numbers and quaternions", Discrete & Computational Geometry, 35 (3): 361–373, arXiv:math/0403023, doi:10.1007/s00454-005-1226-7, MR 2202107, S2CID 1647360
Mandelkern (2016). Mandelkern, Mark (2016), "A constructive version of the Sylvester–Gallai theorem", Acta Mathematica Hungarica, 150: 121–130, arXiv:2402.03662, doi:10.1007/s10474-016-0624-z, MR 3542040, S2CID 124023963
Green & Tao (2013). Green, Ben; Tao, Terence (2013), "On sets defining few ordinary lines", Discrete & Computational Geometry, 50 (2): 409–468, arXiv:1208.4714, doi:10.1007/s00454-013-9518-9, MR 3090525, S2CID 15813230
Basit et al. (2019). Basit, Abdul; Dvir, Zeev; Saraf, Shubhangi; Wolf, Charles (2019), "On the number of ordinary lines determined by sets in complex space", Discrete & Computational Geometry, 61 (4): 778–808, arXiv:1611.08740, doi:10.1007/s00454-018-0039-4, MR 3943495, S2CID 125616042

doi.org (Global: 2^nd place; English: 2^nd place)

Elkies, Pretorius & Swanepoel (2006). Elkies, Noam; Pretorius, Lou M.; Swanepoel, Konrad J. (2006), "Sylvester–Gallai theorems for complex numbers and quaternions", Discrete & Computational Geometry, 35 (3): 361–373, arXiv:math/0403023, doi:10.1007/s00454-005-1226-7, MR 2202107, S2CID 1647360
Borwein & Moser (1990). Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations", Aequationes Mathematicae, 40 (1): 111–135, doi:10.1007/BF02112289, MR 1069788, S2CID 122052678
Steinberg et al. (1944); Erdős (1982). Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021 Erdős, P. (1982), "Personal reminiscences and remarks on the mathematical work of Tibor Gallai" (PDF), Combinatorica, 2 (3): 207–212, doi:10.1007/BF02579228, MR 0698647, S2CID 1135308
Shephard (1968). Shephard, G. C. (1968), "Twenty problems on convex polyhedra, part I", The Mathematical Gazette, 52 (380): 136–156, doi:10.2307/3612678, JSTOR 3612678, MR 0231278, S2CID 250442107
Aigner & Ziegler (2018). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8
Aigner & Ziegler (2018, p. 92); Steenrod's proof was briefly summarized in Steinberg et al. (1944). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Aigner & Ziegler (2018); Pambuccian (2009). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973
Coxeter (1948); Pambuccian (2009). For Steinberg's proof see Steinberg et al. (1944). Coxeter, H. S. M. (1948), "A problem of collinear points", American Mathematical Monthly, 55 (1): 26–28, doi:10.2307/2305324, JSTOR 2305324, MR 0024137 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Mandelkern (2016). Mandelkern, Mark (2016), "A constructive version of the Sylvester–Gallai theorem", Acta Mathematica Hungarica, 150: 121–130, arXiv:2402.03662, doi:10.1007/s10474-016-0624-z, MR 3542040, S2CID 124023963
Mukhopadhyay & Greene (2012). Mukhopadhyay, Asish; Greene, Eugene (2012), "The ordinary line problem revisited", Computational Geometry: Theory and Applications, 45 (3): 127–130, doi:10.1016/j.comgeo.2011.10.003, MR 2853475
Crowe & McKee (1968). Crowe, D. W.; McKee, T. A. (1968), "Sylvester's problem on collinear points", Mathematics Magazine, 41 (1): 30–34, doi:10.2307/2687957, JSTOR 2687957, MR 0235452
Geelen, Gerards & Kapoor (2000). Geelen, J. F.; Gerards, A. M. H.; Kapoor, A. (2000), "The excluded minors for GF(4)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 79 (2): 247–299, doi:10.1006/jctb.2000.1963, MR 1769191, archived from the original (PDF) on 2010-09-24
Beck (1983). Beck, József (1983), "On the lattice property of the plane and some problems of Dirac, Motzkin, and Erdős in combinatorial geometry", Combinatorica, 3 (3–4): 281–297, doi:10.1007/BF02579184, MR 0729781, S2CID 31011939
Green & Tao (2013). Green, Ben; Tao, Terence (2013), "On sets defining few ordinary lines", Discrete & Computational Geometry, 50 (2): 409–468, arXiv:1208.4714, doi:10.1007/s00454-013-9518-9, MR 3090525, S2CID 15813230
Basit et al. (2019). Basit, Abdul; Dvir, Zeev; Saraf, Shubhangi; Wolf, Charles (2019), "On the number of ordinary lines determined by sets in complex space", Discrete & Computational Geometry, 61 (4): 778–808, arXiv:1611.08740, doi:10.1007/s00454-018-0039-4, MR 3943495, S2CID 125616042
Chvátal (2004); Chen (2006); Pambuccian (2009) Chvátal, Vašek (2004), "Sylvester–Gallai theorem and metric betweenness", Discrete & Computational Geometry, 31 (2): 175–195, doi:10.1007/s00454-003-0795-6, MR 2060634 Chen, Xiaomin (2006), "The Sylvester–Chvátal theorem", Discrete & Computational Geometry, 35 (2): 193–199, doi:10.1007/s00454-005-1216-9, MR 2195050 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973

jstor.org (Global: 26^th place; English: 20^th place)

Steinberg et al. (1944); Erdős (1982). Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021 Erdős, P. (1982), "Personal reminiscences and remarks on the mathematical work of Tibor Gallai" (PDF), Combinatorica, 2 (3): 207–212, doi:10.1007/BF02579228, MR 0698647, S2CID 1135308
Shephard (1968). Shephard, G. C. (1968), "Twenty problems on convex polyhedra, part I", The Mathematical Gazette, 52 (380): 136–156, doi:10.2307/3612678, JSTOR 3612678, MR 0231278, S2CID 250442107
Aigner & Ziegler (2018, p. 92); Steenrod's proof was briefly summarized in Steinberg et al. (1944). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Coxeter (1948); Pambuccian (2009). For Steinberg's proof see Steinberg et al. (1944). Coxeter, H. S. M. (1948), "A problem of collinear points", American Mathematical Monthly, 55 (1): 26–28, doi:10.2307/2305324, JSTOR 2305324, MR 0024137 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Crowe & McKee (1968). Crowe, D. W.; McKee, T. A. (1968), "Sylvester's problem on collinear points", Mathematics Magazine, 41 (1): 30–34, doi:10.2307/2687957, JSTOR 2687957, MR 0235452

math-inst.hu (Global: low place; English: low place)

Steinberg et al. (1944); Erdős (1982). Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021 Erdős, P. (1982), "Personal reminiscences and remarks on the mathematical work of Tibor Gallai" (PDF), Combinatorica, 2 (3): 207–212, doi:10.1007/BF02579228, MR 0698647, S2CID 1135308

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

Aigner & Ziegler (2018); Pambuccian (2009). Aigner, Martin; Ziegler, Günter M. (2018), "Chapter 11. Lines in the plane and decomposition of graphs", Proofs from THE BOOK (6th ed.), Springer, Theorem 1, pp. 77–78, doi:10.1007/978-3-662-57265-8_11, ISBN 978-3-662-57265-8 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973
Coxeter (1948); Pambuccian (2009). For Steinberg's proof see Steinberg et al. (1944). Coxeter, H. S. M. (1948), "A problem of collinear points", American Mathematical Monthly, 55 (1): 26–28, doi:10.2307/2305324, JSTOR 2305324, MR 0024137 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973 Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021
Chvátal (2004); Chen (2006); Pambuccian (2009) Chvátal, Vašek (2004), "Sylvester–Gallai theorem and metric betweenness", Discrete & Computational Geometry, 31 (2): 175–195, doi:10.1007/s00454-003-0795-6, MR 2060634 Chen, Xiaomin (2006), "The Sylvester–Chvátal theorem", Discrete & Computational Geometry, 35 (2): 193–199, doi:10.1007/s00454-005-1216-9, MR 2195050 Pambuccian, Victor (2009), "A reverse analysis of the Sylvester–Gallai theorem", Notre Dame Journal of Formal Logic, 50 (3): 245–260, doi:10.1215/00294527-2009-010, MR 2572973

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Elkies, Pretorius & Swanepoel (2006). Elkies, Noam; Pretorius, Lou M.; Swanepoel, Konrad J. (2006), "Sylvester–Gallai theorems for complex numbers and quaternions", Discrete & Computational Geometry, 35 (3): 361–373, arXiv:math/0403023, doi:10.1007/s00454-005-1226-7, MR 2202107, S2CID 1647360
Borwein & Moser (1990). Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations", Aequationes Mathematicae, 40 (1): 111–135, doi:10.1007/BF02112289, MR 1069788, S2CID 122052678
Steinberg et al. (1944); Erdős (1982). Steinberg, R.; Buck, R. C.; Grünwald, T.; Steenrod, N. E. (1944), "Three point collinearity (solution to problem 4065)", American Mathematical Monthly, 51 (3): 169–171, doi:10.2307/2303021, JSTOR 2303021 Erdős, P. (1982), "Personal reminiscences and remarks on the mathematical work of Tibor Gallai" (PDF), Combinatorica, 2 (3): 207–212, doi:10.1007/BF02579228, MR 0698647, S2CID 1135308
Shephard (1968). Shephard, G. C. (1968), "Twenty problems on convex polyhedra, part I", The Mathematical Gazette, 52 (380): 136–156, doi:10.2307/3612678, JSTOR 3612678, MR 0231278, S2CID 250442107
Mandelkern (2016). Mandelkern, Mark (2016), "A constructive version of the Sylvester–Gallai theorem", Acta Mathematica Hungarica, 150: 121–130, arXiv:2402.03662, doi:10.1007/s10474-016-0624-z, MR 3542040, S2CID 124023963
Beck (1983). Beck, József (1983), "On the lattice property of the plane and some problems of Dirac, Motzkin, and Erdős in combinatorial geometry", Combinatorica, 3 (3–4): 281–297, doi:10.1007/BF02579184, MR 0729781, S2CID 31011939
Green & Tao (2013). Green, Ben; Tao, Terence (2013), "On sets defining few ordinary lines", Discrete & Computational Geometry, 50 (2): 409–468, arXiv:1208.4714, doi:10.1007/s00454-013-9518-9, MR 3090525, S2CID 15813230
Basit et al. (2019). Basit, Abdul; Dvir, Zeev; Saraf, Shubhangi; Wolf, Charles (2019), "On the number of ordinary lines determined by sets in complex space", Discrete & Computational Geometry, 61 (4): 778–808, arXiv:1611.08740, doi:10.1007/s00454-018-0039-4, MR 3943495, S2CID 125616042

uwaterloo.ca (Global: 3,153^rd place; English: 2,332^nd place)

math.uwaterloo.ca

Geelen, Gerards & Kapoor (2000). Geelen, J. F.; Gerards, A. M. H.; Kapoor, A. (2000), "The excluded minors for GF(4)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 79 (2): 247–299, doi:10.1006/jctb.2000.1963, MR 1769191, archived from the original (PDF) on 2010-09-24

washington.edu (Global: 1,067^th place; English: 749^th place)

sites.math.washington.edu

For the history of this variation of the problem, see also Grünbaum (1999) Grünbaum, Branko (1999), "Monochromatic intersection points in families of colored lines" (PDF), Geombinatorics, 9 (1): 3–9, MR 1698297

web.archive.org (Global: 1^st place; English: 1^st place)

Geelen, Gerards & Kapoor (2000). Geelen, J. F.; Gerards, A. M. H.; Kapoor, A. (2000), "The excluded minors for GF(4)-representable matroids" (PDF), Journal of Combinatorial Theory, Series B, 79 (2): 247–299, doi:10.1006/jctb.2000.1963, MR 1769191, archived from the original (PDF) on 2010-09-24

Sylvester–Gallai theorem (English Wikipedia)

acm.org (Global: 1,185th place; English: 840th place)

dl.acm.org

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

arxiv.org (Global: 69th place; English: 59th place)

doi.org (Global: 2nd place; English: 2nd place)

jstor.org (Global: 26th place; English: 20th place)