Probabilistic combinatorics and the recent work of Peter Keevash

Gowers, W.

doi:10.1090/bull/1553

Probabilistic combinatorics and the recent work of Peter Keevash

Author: W. T. Gowers
Journal: Bull. Amer. Math. Soc. 54 (2017), 107-116
MSC (2010): Primary 05-02
DOI: https://doi.org/10.1090/bull/1553
Published electronically: September 14, 2016
MathSciNet review: 3584100
Full-text PDF Free Access

References

Miklós Ajtai, János Komlós, and Endre Szemerédi, A dense infinite Sidon sequence, European J. Combin. 2 (1981), no. 1, 1–11. MR 611925, DOI https://doi.org/10.1016/S0195-6698%2881%2980014-5
Noga Alon and Joel H. Spencer, The probabilistic method, 3rd ed., Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., Hoboken, NJ, 2008. With an appendix on the life and work of Paul Erdős. MR 2437651
P. Erdös, Some remarks on the theory of graphs, Bull. Amer. Math. Soc. 53 (1947), 292–294. MR 19911, DOI https://doi.org/10.1090/S0002-9904-1947-08785-1
P. Erdős, Graph theory and probability, Canadian J. Math. 11 (1959), 34–38. MR 102081, DOI https://doi.org/10.4153/CJM-1959-003-9
Misha Gromov, Spaces and questions, Geom. Funct. Anal. Special Volume (2000), 118–161. GAFA 2000 (Tel Aviv, 1999). MR 1826251

Misha Gromov, Random walks in random groups, Geom. Funct. Anal. 13 (2003), 73–146.

G. Kalai, Designs exist! [after Peter Keevash], http://www.bourbaki.ens.fr/TEXTES/ 1100.pdf, Séminaire Bourbaki 67ème année, 2014-2015, no. 1100, 2015.

P. Keevash, The existence of designs, arxiv:1401.3665 [math.CO], 2014.

Torsten Mütze, Proof of the middle levels conjecture, Proc. Lond. Math. Soc. (3) 112 (2016), no. 4, 677–713. MR 3483129, DOI https://doi.org/10.1112/plms/pdw004

Vojtěch Rödl, On a packing and covering problem, European J. Combin. 6 (1985), no. 1, 69–78. MR 793489, DOI https://doi.org/10.1016/S0195-6698%2885%2980023-8

Richard M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms, J. Combinatorial Theory Ser. A 13 (1972), 220–245. MR 304203, DOI https://doi.org/10.1016/0097-3165%2872%2990028-3

Richard M. Wilson, An existence theory for pairwise balanced designs. II. The structure of PBD-closed sets and the existence conjectures, J. Combinatorial Theory Ser. A 13 (1972), 246–273. MR 304204, DOI https://doi.org/10.1016/0097-3165%2872%2990029-5

Richard M. Wilson, An existence theory for pairwise balanced designs. III. Proof of the existence conjectures, J. Combinatorial Theory Ser. A 18 (1975), 71–79. MR 366695, DOI https://doi.org/10.1016/0097-3165%2875%2990067-9