# The apparent structure of dense Sidon sets

@inproceedings{Eberhard2021TheAS, title={The apparent structure of dense Sidon sets}, author={Sean Eberhard and Freddie Manners}, year={2021} }

. The correspondence between perfect diﬀerence sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets of abelian groups come from projective planes through a similar construction. We classify the Sidon sets arising in this man- ner from desarguesian planes and ﬁnd essentially no new examples. There are many further examples arising from nondesarguesian planes. We conjecture that all dense Sidon sets arise from ﬁnite…

## 2 Citations

Extremal Sidon sets are Fourier uniform, with applications to partition regularity

- Mathematics
- 2021

Generalising results of Erdős-Freud and Lindström, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing…

Paley-like graphs for the Ramsey number $r(C_4,K_t)$

- Mathematics
- 2021

A famous conjecture of Erdős asserts that the Ramsey number r(C4,Kt) is upperbounded by O(t2−ε) for some ε > 0, but the best known upper bound is r(C4,Kt) = O(t2/ log t), due to Szemerédi and…

## References

SHOWING 1-10 OF 39 REFERENCES

Planar division neo-rings

- Mathematics
- 1955

Introduction. The notion of a division ring can be generalized to give a system whose addition is not necessarily associative, but which retains the property of coordinatizing an affine plane. Such a…

Planar Functions and Planes of Lenz-Barlotti Class II

- MathematicsDes. Codes Cryptogr.
- 1997

Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes, and which cannot be obtained by derivation or lifting.

Proof of the prime power conjecture for projective planes of order $n$ with Abelian collineation groups of order $n^2$

- Mathematics
- 2001

Let G be an abelian collineation group of order n 2 of a projective plane of order n. We show that n must be a prime power, and that the p-rank of G is at least b + 1 if n = p b for an odd prime p.

ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS

- Mathematics
- 2002

Let a,<&<... be a sequence of positive integers, and suppose that the suma czi+lzi (where i ,<j) are all different. Such sequences, called B, sequences by Sidont, occur in the theory of Fourier…

Handbook of Finite Translation Planes

- Mathematics
- 2007

Preface and Acknowledgments An Overview Translation Plane Structure Theory Partial Spreads and Translation Nets Partial Spreads and Generalizations Quasifields Derivation Frequently Used Tools…

A Simple Proof of a Theorem of Schur

- Mathematics
- 1998

I. J. A. Gallian and J. Van Buskirk, The number of homomorphisms from Zm into Z,, Amer. Math. Momhly 91 (1984) 196-197. 2. J. A. Gallian and D. S. Jungreis, Homomorphisms from Zm[i) into Z,[i) and…

A theorem in finite projective geometry and some applications to number theory

- Mathematics
- 1938

A point in a finite projective plane PG(2, pn), may be denoted by the symbol (Xl, X2, X3), where the coordinates x1, X2, X3 are marks of a Galois field of order pn, GF(pn). The symbol (0, 0, 0) is…

A Remark on Infinite Sidon Sets

- Mathematics
- 2011

Resumen . Un conjunto de Sidon es un subconjunto de los enteros con la pro-piedad que la suma de cada dos elementos es distinta. En 1998, I. Ruzsa diouna construccion probabilstica de un conjunto…