List of conjectures by Paul Erdős (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "List of conjectures by Paul Erdős" in English language version.

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Erdős, P.; Hajnal, A. (1989), "Ramsey-type theorems", Combinatorics and complexity (Chicago, IL, 1987), Discrete Applied Mathematics, 25 (1–2): 37–52, doi:10.1016/0166-218X(89)90045-0, MR 1031262.
Oler, Norman (1961), "A finite packing problem", Canadian Mathematical Bulletin, 4 (2): 153–155, doi:10.4153/CMB-1961-018-7, MR 0133065.
Lagarias, Jeffrey C. (2009), "Ternary expansions of powers of 2", Journal of the London Mathematical Society, Second Series, 79 (3): 562–588, arXiv:math/0512006, doi:10.1112/jlms/jdn080, MR 2506687, S2CID 15615918
Moreira, J.; Richter, F. K.; Robertson, D. (2019), "A proof of a sumset conjecture of Erdős", Annals of Mathematics, 189 (2): 605–652, arXiv:1803.00498, doi:10.4007/annals.2019.189.2.4, MR 3919363, S2CID 119158401, Zbl 1407.05236.
Hajnal, A.; Szemerédi, E. (1970), "Proof of a conjecture of P. Erdős", Combinatorial theory and its applications, II (Proc. Colloq., Balatonfüred, 1969), North-Holland, pp. 601–623, MR 0297607.
Sárközy, A. (1978), "On difference sets of sequences of integers. II", Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, 21: 45–53 (1979), MR 0536201.
Deza, M. (1974), "Solution d'un problème de Erdős-Lovász", Journal of Combinatorial Theory, Series B (in French), 16 (2): 166–167, doi:10.1016/0095-8956(74)90059-8, MR 0337635.
Luca, Florian (2001), "On a conjecture of Erdős and Stewart", Mathematics of Computation, 70 (234): 893–896, Bibcode:2001MaCom..70..893L, doi:10.1090/S0025-5718-00-01178-9, MR 1677411.
Sapozhenko, A. A. (2003), "The Cameron-Erdős conjecture", Doklady Akademii Nauk, 393 (6): 749–752, MR 2088503. Green, Ben (2004), "The Cameron-Erdős conjecture", Bulletin of the London Mathematical Society, 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR 2083752, S2CID 119615076.
Tao, Terence (2016). "The Erdős discrepancy problem". Discrete Analysis: 1–29. arXiv:1509.05363. doi:10.19086/da.609. ISSN 2397-3129. MR 3533300. S2CID 59361755.
Sárközy, A. (1985), "On divisors of binomial coefficients. I", Journal of Number Theory, 20 (1): 70–80, doi:10.1016/0022-314X(85)90017-4, MR 0777971

arxiv.org

Lagarias, Jeffrey C. (2009), "Ternary expansions of powers of 2", Journal of the London Mathematical Society, Second Series, 79 (3): 562–588, arXiv:math/0512006, doi:10.1112/jlms/jdn080, MR 2506687, S2CID 15615918
Moreira, J.; Richter, F. K.; Robertson, D. (2019), "A proof of a sumset conjecture of Erdős", Annals of Mathematics, 189 (2): 605–652, arXiv:1803.00498, doi:10.4007/annals.2019.189.2.4, MR 3919363, S2CID 119158401, Zbl 1407.05236.
Lee, Choongbum (2017), "Ramsey numbers of degenerate graphs", Annals of Mathematics, 185 (3): 791–829, arXiv:1505.04773, doi:10.4007/annals.2017.185.3.2, S2CID 7974973
Croot, Ernest S. III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S. III (2003), "On a coloring conjecture about unit fractions", Annals of Mathematics, 157 (2): 545–556, arXiv:math.NT/0311421, Bibcode:2003math.....11421C, doi:10.4007/annals.2003.157.545, S2CID 13514070.
Sapozhenko, A. A. (2003), "The Cameron-Erdős conjecture", Doklady Akademii Nauk, 393 (6): 749–752, MR 2088503. Green, Ben (2004), "The Cameron-Erdős conjecture", Bulletin of the London Mathematical Society, 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR 2083752, S2CID 119615076.
Aharoni, Ron; Berger, Eli (2009), "Menger's Theorem for infinite graphs", Inventiones Mathematicae, 176 (1): 1–62, arXiv:math/0509397, Bibcode:2009InMat.176....1A, doi:10.1007/s00222-008-0157-3, S2CID 15355399.
Guth, Larry; Katz, Nets H. (2015), "On the Erdős distinct distances problem in the plane", Annals of Mathematics, Second series, 181 (1): 155–190, arXiv:1011.4105, doi:10.4007/annals.2015.181.1.2.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016), "Large gaps between consecutive prime numbers", Annals of Mathematics, Second series, 183 (3): 935–974, arXiv:1408.4505, doi:10.4007/annals.2016.183.3.4
Tao, Terence (2016). "The Erdős discrepancy problem". Discrete Analysis: 1–29. arXiv:1509.05363. doi:10.19086/da.609. ISSN 2397-3129. MR 3533300. S2CID 59361755.
Lichtman, Jared Duker (2023). "A proof of the Erdős primitive set conjecture". Forum of Mathematics, Pi. 11. arXiv:2202.02384. doi:10.1017/fmp.2023.16.
Janzer, Oliver; Sudakov, Benny (2022-04-26). "Resolution of the Erdős-Sauer problem on regular subgraphs". arXiv:2204.12455 [math.CO].

doi.org

Erdős, P.; Hajnal, A. (1989), "Ramsey-type theorems", Combinatorics and complexity (Chicago, IL, 1987), Discrete Applied Mathematics, 25 (1–2): 37–52, doi:10.1016/0166-218X(89)90045-0, MR 1031262.
Oler, Norman (1961), "A finite packing problem", Canadian Mathematical Bulletin, 4 (2): 153–155, doi:10.4153/CMB-1961-018-7, MR 0133065.
Lagarias, Jeffrey C. (2009), "Ternary expansions of powers of 2", Journal of the London Mathematical Society, Second Series, 79 (3): 562–588, arXiv:math/0512006, doi:10.1112/jlms/jdn080, MR 2506687, S2CID 15615918
Moreira, J.; Richter, F. K.; Robertson, D. (2019), "A proof of a sumset conjecture of Erdős", Annals of Mathematics, 189 (2): 605–652, arXiv:1803.00498, doi:10.4007/annals.2019.189.2.4, MR 3919363, S2CID 119158401, Zbl 1407.05236.
Lee, Choongbum (2017), "Ramsey numbers of degenerate graphs", Annals of Mathematics, 185 (3): 791–829, arXiv:1505.04773, doi:10.4007/annals.2017.185.3.2, S2CID 7974973
Deza, M. (1974), "Solution d'un problème de Erdős-Lovász", Journal of Combinatorial Theory, Series B (in French), 16 (2): 166–167, doi:10.1016/0095-8956(74)90059-8, MR 0337635.
da Silva, Dias; A., J.; Hamidoune, Y. O. (1994), "Cyclic spaces for Grassmann derivatives and additive theory", Bulletin of the London Mathematical Society, 26 (2): 140–146, doi:10.1112/blms/26.2.140.
Croot, Ernest S. III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S. III (2003), "On a coloring conjecture about unit fractions", Annals of Mathematics, 157 (2): 545–556, arXiv:math.NT/0311421, Bibcode:2003math.....11421C, doi:10.4007/annals.2003.157.545, S2CID 13514070.
Luca, Florian (2001), "On a conjecture of Erdős and Stewart", Mathematics of Computation, 70 (234): 893–896, Bibcode:2001MaCom..70..893L, doi:10.1090/S0025-5718-00-01178-9, MR 1677411.
Sapozhenko, A. A. (2003), "The Cameron-Erdős conjecture", Doklady Akademii Nauk, 393 (6): 749–752, MR 2088503. Green, Ben (2004), "The Cameron-Erdős conjecture", Bulletin of the London Mathematical Society, 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR 2083752, S2CID 119615076.
Aharoni, Ron; Berger, Eli (2009), "Menger's Theorem for infinite graphs", Inventiones Mathematicae, 176 (1): 1–62, arXiv:math/0509397, Bibcode:2009InMat.176....1A, doi:10.1007/s00222-008-0157-3, S2CID 15355399.
Guth, Larry; Katz, Nets H. (2015), "On the Erdős distinct distances problem in the plane", Annals of Mathematics, Second series, 181 (1): 155–190, arXiv:1011.4105, doi:10.4007/annals.2015.181.1.2.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016), "Large gaps between consecutive prime numbers", Annals of Mathematics, Second series, 183 (3): 935–974, arXiv:1408.4505, doi:10.4007/annals.2016.183.3.4
Tao, Terence (2016). "The Erdős discrepancy problem". Discrete Analysis: 1–29. arXiv:1509.05363. doi:10.19086/da.609. ISSN 2397-3129. MR 3533300. S2CID 59361755.
Sárközy, A. (1985), "On divisors of binomial coefficients. I", Journal of Number Theory, 20 (1): 70–80, doi:10.1016/0022-314X(85)90017-4, MR 0777971
Ramaré, Olivier; Granville, Andrew (1996), "Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients", Mathematika, 43 (1): 73–107, doi:10.1112/S0025579300011608
Lichtman, Jared Duker (2023). "A proof of the Erdős primitive set conjecture". Forum of Mathematics, Pi. 11. arXiv:2202.02384. doi:10.1017/fmp.2023.16.

gilkalai.wordpress.com

Kalai, Gil (May 22, 2015), "Choongbum Lee proved the Burr-Erdős conjecture", Combinatorics and more, retrieved 2015-05-22

harvard.edu

ui.adsabs.harvard.edu

Croot, Ernest S. III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S. III (2003), "On a coloring conjecture about unit fractions", Annals of Mathematics, 157 (2): 545–556, arXiv:math.NT/0311421, Bibcode:2003math.....11421C, doi:10.4007/annals.2003.157.545, S2CID 13514070.
Luca, Florian (2001), "On a conjecture of Erdős and Stewart", Mathematics of Computation, 70 (234): 893–896, Bibcode:2001MaCom..70..893L, doi:10.1090/S0025-5718-00-01178-9, MR 1677411.
Aharoni, Ron; Berger, Eli (2009), "Menger's Theorem for infinite graphs", Inventiones Mathematicae, 176 (1): 1–62, arXiv:math/0509397, Bibcode:2009InMat.176....1A, doi:10.1007/s00222-008-0157-3, S2CID 15355399.

numberphile.com

Haran, Brady (16 June 2022). "Primes and Primitive Sets". Numberphile. Retrieved 2022-06-21.

quantamagazine.org

Houston-Edwards, Kelsey (5 April 2021), "Mathematicians Settle Erdős Coloring Conjecture", Quanta Magazine, retrieved 2021-04-05
Cepelewicz, Jordana (2022-06-06). "Graduate Student's Side Project Proves Prime Number Conjecture". Quanta Magazine. Retrieved 2022-06-06.
"New Proof Shows When Structure Must Emerge in Graphs". Quanta Magazine. 2022-06-23. Retrieved 2022-06-26.

semanticscholar.org

api.semanticscholar.org

Lagarias, Jeffrey C. (2009), "Ternary expansions of powers of 2", Journal of the London Mathematical Society, Second Series, 79 (3): 562–588, arXiv:math/0512006, doi:10.1112/jlms/jdn080, MR 2506687, S2CID 15615918
Moreira, J.; Richter, F. K.; Robertson, D. (2019), "A proof of a sumset conjecture of Erdős", Annals of Mathematics, 189 (2): 605–652, arXiv:1803.00498, doi:10.4007/annals.2019.189.2.4, MR 3919363, S2CID 119158401, Zbl 1407.05236.
Lee, Choongbum (2017), "Ramsey numbers of degenerate graphs", Annals of Mathematics, 185 (3): 791–829, arXiv:1505.04773, doi:10.4007/annals.2017.185.3.2, S2CID 7974973
Croot, Ernest S. III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S. III (2003), "On a coloring conjecture about unit fractions", Annals of Mathematics, 157 (2): 545–556, arXiv:math.NT/0311421, Bibcode:2003math.....11421C, doi:10.4007/annals.2003.157.545, S2CID 13514070.
Sapozhenko, A. A. (2003), "The Cameron-Erdős conjecture", Doklady Akademii Nauk, 393 (6): 749–752, MR 2088503. Green, Ben (2004), "The Cameron-Erdős conjecture", Bulletin of the London Mathematical Society, 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR 2083752, S2CID 119615076.
Aharoni, Ron; Berger, Eli (2009), "Menger's Theorem for infinite graphs", Inventiones Mathematicae, 176 (1): 1–62, arXiv:math/0509397, Bibcode:2009InMat.176....1A, doi:10.1007/s00222-008-0157-3, S2CID 15355399.
Tao, Terence (2016). "The Erdős discrepancy problem". Discrete Analysis: 1–29. arXiv:1509.05363. doi:10.19086/da.609. ISSN 2397-3129. MR 3533300. S2CID 59361755.

worldcat.org

search.worldcat.org

Tao, Terence (2016). "The Erdős discrepancy problem". Discrete Analysis: 1–29. arXiv:1509.05363. doi:10.19086/da.609. ISSN 2397-3129. MR 3533300. S2CID 59361755.

zbmath.org

Moreira, J.; Richter, F. K.; Robertson, D. (2019), "A proof of a sumset conjecture of Erdős", Annals of Mathematics, 189 (2): 605–652, arXiv:1803.00498, doi:10.4007/annals.2019.189.2.4, MR 3919363, S2CID 119158401, Zbl 1407.05236.