Bibliography
Kakeya Sets with Multiplicity
Ball, S., and Blokhuis, A. (1998). "An Easier Proof of the Maximal Arcs Conjecture." Proceedings of the American Mathematical Society 126(11): 3377–3380.
Ball, S., Blokhuis, A., Brouwer, A. E., Storme, L., and Szőnyi, T. (1999). "On the Number of Slopes of the Graph of a Function Defined on a Finite Field." Journal of Combinatorial Theory, Series A 86(1): 187–196.
Ball, S., Blokhuis, A., and Mazzocca, F. (1997). "Maximal Arcs in Desarguesian Planes of Odd Order Do Not Exist." Combinatorica 17(1): 31–41.
Barlotti, A. (1955). "Sui -archi di un piano lineare finito." Bollettino dell'Unione Matematica Italiana (3) 10: 498–506.
Bichara, A., and Korchmáros, G. (1982). "Note on -Sets in a Galois Plane of Order ." Annals of Discrete Mathematics 14: 117–122.
Blokhuis, A., De Boeck, M., Mazzocca, F., and Storme, L. (2014). "The Kakeya Problem: A Gap in the Spectrum and Classification of the Smallest Examples." Designs, Codes and Cryptography 72(1): 21–31.
Blokhuis, A., and Mazzocca, F. (2008). "The Finite Field Kakeya Problem." In M. Grötschel and G. O. H. Katona (eds.), Building Bridges: Between Mathematics and Computer Science. Bolyai Society Mathematical Studies 19. Berlin: Springer, 205–218.
Cossu, A. (1961). "Su alcune proprietà dei -archi di un piano proiettivo sopra un corpo finito." Rendiconti di Matematica e delle sue Applicazioni (5) 20: 271–277.
Denniston, R. H. F. (1969). "Some Maximal Arcs in Finite Projective Planes." Journal of Combinatorial Theory 6(3): 317–319.
Dhar, M., Dvir, Z., and Lund, B. (2021). "Simple Proofs for Furstenberg Sets over Finite Fields." Discrete Analysis 2021:22.
Dover, J. M., Mellinger, K. E., and Scott, K. E. (2014). "Minimal Kakeya Sets." Journal of Combinatorial Designs 22(2): 95–104.
Dvir, Z. (2009). "On the Size of Kakeya Sets in Finite Fields." Journal of the American Mathematical Society 22(4): 1093–1097.
Ellenberg, J. S., and Erman, D. (2016). "Furstenberg Sets and Furstenberg Schemes over Finite Fields." Algebra & Number Theory 10(7): 1415–1436.
Guth, L. (2016). Polynomial Methods in Combinatorics. University Lecture Series 64. Providence, RI: American Mathematical Society.
Hamilton, N., and Mathon, R. (2004). "On the Spectrum of Non-Denniston Maximal Arcs in ." European Journal of Combinatorics 25(3): 415–421.
Hirschfeld, J. W. P. (1998). Projective Geometries over Finite Fields, 2nd edn. Oxford: Clarendon Press.
Lidl, R., and Niederreiter, H. (1997). Finite Fields, 2nd edn. Encyclopedia of Mathematics and Its Applications 20. Cambridge: Cambridge University Press.
Mathon, R. (2002). "New Maximal Arcs in Desarguesian Planes." Journal of Combinatorial Theory, Series A 97(2): 353–368.
Rédei, L. (1970). Lückenhafte Polynome über endlichen Körpern. Basel: Birkhäuser. (English translation: Lacunary Polynomials over Finite Fields, Amsterdam: North-Holland, 1973.)
Segre, B. (1955). "Ovals in a Finite Projective Plane." Canadian Journal of Mathematics 7: 414–416.
Szőnyi, T. (1996). "On the Number of Directions Determined by a Set of Points in an Affine Galois Plane." Journal of Combinatorial Theory, Series A 74(1): 141–146.
Thas, J. A. (1974). "Construction of Maximal Arcs and Partial Geometries." Geometriae Dedicata 3: 61–64.
Three Lemmas. The Polynomial Method in Combinatorics, from the Nullstellensatz to Cap Sets. Companion dissertation by the same author; Chapter 7 treats punctured Kakeya sets.
Wolff, T. (1999). "Recent Work Connected with the Kakeya Problem." In H. Rossi (ed.), Prospects in Mathematics (Princeton, NJ, 1996). Providence, RI: American Mathematical Society, 129–162.