In this page you will find a (non-exhaustive) list of my favourite books, research papers, articles, blog posts, etc.
Books and Surveys
1. Incidence Geometry
- Linear Geometry by Gruenberg and Weir
- Projective Geometry: An Introduction by Rey Casse
- Incidence Geometry by Eric Moorhouse
- An Introduction to Finite Geometry by Simeon Ball and Zsusza Weiner
- An Introduction to Incidence Geometry by Bart De Bruyn
- Projective and Polar Spaces by Peter Cameron
- Projective Geometry: From Foundations to Applications by Albrecht Beutelspacher and Ute Rosenbaum
- A Geometrical Picture Book by Burkard Polster
- Finite Geometry and Combinatorial Applications by Simeon Ball
- Prehistory and History of Polar Spaces and of Generalized Polygons, by Francis Buekenhout
- Blocking sets in projective and affine planes, by Aart Blokhuis (notes for the internsive course, Ghent, April 14-24, 1998)
Also see Elements of Finite Geometry.
- A Course in Combinatorics by Van Lint and Wilson
- Discrete Mathematics: Elementary and Beyond by Lovasz
- Invitation to Discrete Mathematics by Matousek and Nesetril
- Combinatorics: Topics, Techniques, Algorithms by Cameron
- Linear Algebra Methods in Combinatorics by Babai and Frankl
- Algebraic Graph Theory by Chris Godsil and Gordon Royle
- Algebraic Combinatorics by Chris Godsil
- Thirty Three Miniatures by Jiřì Matoušek
- Extremal Combinatorics by Stasys Jukna
- Eigenvalue techniques in design and graph theory by W. H. Haemers (PhD thesis, 1979).
3. Polynomial Methods
- Polynomials in finite geometries and combinatorics by Aart Blokhuis
- Tools from higher algebra by Noga Alon
- The Jamison method in galois geometries by A. A. Bruen and J. C. Fisher
- Polynomials in Finite Geometries and The Polynomial Method in Galois Geometries by Simeon Ball
- Polynomials in finite geometries and Applications of Polynomials over Finite Fields by Peter Sziklai
- Discrete mathematics: methods and challenges by Noga Alon
- Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory by Terence Tao
- Incidence Theorems and Their Applications by Zeev Dvir
- The polynomial method in additive combinatorics by Gyula Károlyi
- Unexpected applications of polynomials in combinatorics and Polynomial Methods in Combinatorics by Larry Guth
- The Polynomial Method in Finite Geometry by Simeon Ball and Aart Blokhuis
- P. Erdős and G. Szekeres, A combinatorial problem in geometry. Compositio Mathematica, 2 (1935), 463–470.
- R. C. Bose, A Note on Fisher’s Inequality for Balanced Incomplete Block Designs. Ann. Math. Statist. 20 (1949), 619-620.
- B. Segre, Ovals in a finite projective plane. Canad. J. Math. 7 (1955), 414-416.
- R. C. Bose. Strongly regular graphs, partial geometries and partially balanced designs. Pacific J. Math. 13 (1963), 389–419.
- F. Buekenhout and E. Shult. On the foundations of polar geometry. Geometriae Dedicata 3 (1974), 155-170.
- T. H. Koornwinder, A note on the absolute bound for systems of lines, Indag. Math. 38 (1976) 152–153.
- P. J. Cameron, J.M. Goethals, J.J. Seidel, E.E. Shult, Line graphs, root systems, and elliptic geometry. J. Algebra, 43 (1976), 305–327.
- R. E. Jamison, Covering finite fields with cosets of subspaces, J. Comb. Theory Ser. A 22 (1977), 253-266.
- A. E. Brouwer and A. Schrijver, The blocking number of an affine space. J. Comb. Theory Ser. A 24 (1978), 251-253.
- P. J. Cameron, Dual polar spaces. Geom. Dedicata 12 (1982), 75–85.
- A. M. Cohen and J. Tits, On Generalized Hexagons and a Near Polygon whose Lines have Three Points. Eur. J. Comb. 6 (1985), 13-27.
- A. Nilli, On the second eigenvalue of a graph. Discrete Math. 91 (1991), 207-210.
- A. A. Bruen, Polynomial multiplicities over finite fields and intersection sets. J. Combin. Theory Ser. A 60 (1992), 19-33.
- N. Alon and Z. Furedi, Covering the cube by affine hyperplanes. Eur. J. Comb. 14 (1993), 79-83.
- J. Kahn and G. Kalai, A counterexample to Borsuk’s conjecture. Bull. Amer. Math. Soc. 29 (1993), 60–62.
- A. Blokhuis, On the size of a blocking set in . Combinatorica 14 (1994), 111-114.
- W. H. Haemers, Interlacing Eigenvalues and Graphs. Linear Algebra Appl. 226 (1995), 593-616.
- F. Lazebnik, V. A. Ustimenko and A. J. Woldar, A new series of dense graphs of high girth. Bulletin of the AMS 32 (1995), 73-79.
- N. Alon, Combinatorial Nullstellensatz. Combin. Probab. Comput. 8 (1999), 7-29.
- B. Bagchi and S. P. Inamdar, Projective Geometric Codes. J. Combin. Theory, Ser. A 99 (2002), 128–142.
- B. L. Davis and D. Maclagan, The card game SET. Math. Intelligencer, 25 18 (2003), 33-40.
- Z. Dvir, On the size of Kakeya sets in finite fields. J. Amer. Math. Soc. 22 (2009), 1093-1097
- S. Ball, On sets of vectors of a finite vector space in which every subset of basis size is a basis. J. Eur. Math. Soc. 14(3) (2012), 733–748. video
- A. Bondarenko, On Borsuk’s conjecture for two-distance sets. Discrete Comput. Geom. 51 (3) (2014), 509-515.
- P. L. Clark, A. Forrow and J. R. Schmitt, Warning’s second theorem with restricted variables. Combinatorica.
- J. Ellenberg and D. Gijswijt, On large subsets of with no three-term arithmetic progression. Ann. of Math. 185 (2017), 339–343.
- How to recognise that the polynomial method might work
- Important formulas in combinatorics
- Where have you used computer programming in your career as an (applied/pure) mathematician?
- Which math paper maximizes the ratio (importance)/(length)?
- Linear Algebra Proofs in Combinatorics?
- Too old for advanced mathematics?
- What are some active areas of research within combinatorics?
- What are some classic papers in mathematics?
- How do you solve the IMO’s 2007 Problem 6?
- Photography, in “Art in the Life of Mathematicians”, by Izabella Laba.
- The wrong way to treat child geniuses, by Jordan Ellenberg.
- One mathematics, by László Lovász.
- What is good mathematics? by Terence Tao.
- What is Combinatorics? (A collection of quotes by Igor Pak).
- Paul Erdos and the Probabilistic Method, by Noga Alon.
- The Many Lives of Lattice Theory, by Gian-Carlo Rota.
- The Many Names of (7, 3, 1), by Ezra Brown.
- A brief history of the classification of finite simple groups, by Ronald Solomon.
- A design dilemma solved minus designs, by Erica Klarreich.
- `Outsiders’ Crack 50-year-old Math Problem, by Erica Klarreich.
- Interview with Endre Szemerédi, by Martin Raussen and Christian Skau.
- On an early paper of Maryam Mirzakhani, by Bill Martin.
- Celebrating Sharadchandra Shrikhande, the Mathematician who disproved Euler, by Nithyanand Rao.
- How the upper bound conjecture was proved, by Richard P. Stanley.